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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 69360.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69360.b1 | 69360j4 | \([0, -1, 0, -28298976, -57933997344]\) | \(50700519510140162/2295\) | \(113450436311040\) | \([2]\) | \(2654208\) | \(2.6259\) | |
| 69360.b2 | 69360j3 | \([0, -1, 0, -1965296, -691022880]\) | \(16981825082402/5646560625\) | \(279130617238775040000\) | \([2]\) | \(2654208\) | \(2.6259\) | |
| 69360.b3 | 69360j2 | \([0, -1, 0, -1768776, -904679424]\) | \(24759905519524/5267025\) | \(130184375666918400\) | \([2, 2]\) | \(1327104\) | \(2.2793\) | |
| 69360.b4 | 69360j1 | \([0, -1, 0, -98356, -17352320]\) | \(-17029316176/11275335\) | \(-69672749199517440\) | \([2]\) | \(663552\) | \(1.9327\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 69360.b have rank \(1\).
Complex multiplication
The elliptic curves in class 69360.b do not have complex multiplication.Modular form 69360.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
