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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 388080.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.bq1 | 388080bq7 | \([0, 0, 0, -37566151203, 2802484161915298]\) | \(16689299266861680229173649/2396798250\) | \(841990507405673472000\) | \([2]\) | \(382205952\) | \(4.3378\) | |
| 388080.bq2 | 388080bq8 | \([0, 0, 0, -2409631203, 41364107187298]\) | \(4404531606962679693649/444872222400201750\) | \(156282736049826257776278528000\) | \([2]\) | \(382205952\) | \(4.3378\) | |
| 388080.bq3 | 388080bq6 | \([0, 0, 0, -2347891203, 43788550551298]\) | \(4074571110566294433649/48828650062500\) | \(17153408653422725376000000\) | \([2, 2]\) | \(191102976\) | \(3.9913\) | |
| 388080.bq4 | 388080bq5 | \([0, 0, 0, -529277763, -4677499007678]\) | \(46676570542430835889/106752955783320\) | \(37502103235870199405445120\) | \([2]\) | \(127401984\) | \(3.7885\) | |
| 388080.bq5 | 388080bq4 | \([0, 0, 0, -464362563, 3834137422402]\) | \(31522423139920199089/164434491947880\) | \(57765513351067245664174080\) | \([2]\) | \(127401984\) | \(3.7885\) | |
| 388080.bq6 | 388080bq3 | \([0, 0, 0, -142891203, 721813551298]\) | \(-918468938249433649/109183593750000\) | \(-38355981569136000000000000\) | \([2]\) | \(95551488\) | \(3.6447\) | |
| 388080.bq7 | 388080bq2 | \([0, 0, 0, -45236163, -14532658238]\) | \(29141055407581489/16604321025600\) | \(5833065292613442345369600\) | \([2, 2]\) | \(63700992\) | \(3.4420\) | |
| 388080.bq8 | 388080bq1 | \([0, 0, 0, 11211837, -1809279038]\) | \(443688652450511/260789760000\) | \(-91614929353609052160000\) | \([2]\) | \(31850496\) | \(3.0954\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.bq do not have complex multiplication.Modular form 388080.2.a.bq
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 4 & 6 & 12 \\ 4 & 1 & 2 & 3 & 12 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 12 & 3 & 6 & 1 & 4 & 12 & 2 & 4 \\ 3 & 12 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
