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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 87120.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.c1 | 87120bm4 | \([0, 0, 0, -1307163, -574270598]\) | \(186779563204/360855\) | \(477217458128378880\) | \([2]\) | \(1966080\) | \(2.2812\) | |
| 87120.c2 | 87120bm3 | \([0, 0, 0, -1089363, 435319522]\) | \(108108036004/658845\) | \(871298267172664320\) | \([2]\) | \(1966080\) | \(2.2812\) | |
| 87120.c3 | 87120bm2 | \([0, 0, 0, -109263, -2393138]\) | \(436334416/245025\) | \(81009136410681600\) | \([2, 2]\) | \(983040\) | \(1.9346\) | |
| 87120.c4 | 87120bm1 | \([0, 0, 0, 26862, -296813]\) | \(103737344/61875\) | \(-1278553289310000\) | \([2]\) | \(491520\) | \(1.5880\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.c have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.c do not have complex multiplication.Modular form 87120.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
