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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 44400.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44400.b1 | 44400bo4 | \([0, -1, 0, -143327243408, 20885372686629312]\) | \(5087799435928552778197163696329/125914832087040\) | \(8058549253570560000000\) | \([4]\) | \(113541120\) | \(4.6490\) | |
| 44400.b2 | 44400bo2 | \([0, -1, 0, -8957963408, 326335369509312]\) | \(1242142983306846366056931529/6179359141291622400\) | \(395478985042663833600000000\) | \([2, 2]\) | \(56770560\) | \(4.3025\) | |
| 44400.b3 | 44400bo3 | \([0, -1, 0, -8806411408, 337909698853312]\) | \(-1180159344892952613848670409/87759036144023189760000\) | \(-5616578313217484144640000000000\) | \([2]\) | \(113541120\) | \(4.6490\) | |
| 44400.b4 | 44400bo1 | \([0, -1, 0, -569355408, 4917465381312]\) | \(318929057401476905525449/21353131537921474560\) | \(1366600418426974371840000000\) | \([2]\) | \(28385280\) | \(3.9559\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44400.b have rank \(1\).
Complex multiplication
The elliptic curves in class 44400.b do not have complex multiplication.Modular form 44400.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
