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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 292215bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 292215.bd4 | 292215bd1 | \([1, 0, 1, -27954, -475169]\) | \(1363569097969/734582625\) | \(1301357929727625\) | \([2]\) | \(1351680\) | \(1.5913\) | \(\Gamma_0(N)\)-optimal |
| 292215.bd2 | 292215bd2 | \([1, 0, 1, -347999, -78950203]\) | \(2630872462131649/3645140625\) | \(6457588970765625\) | \([2, 2]\) | \(2703360\) | \(1.9379\) | |
| 292215.bd3 | 292215bd3 | \([1, 0, 1, -250594, -124068199]\) | \(-982374577874929/3183837890625\) | \(-5640363037353515625\) | \([2]\) | \(5406720\) | \(2.2844\) | |
| 292215.bd1 | 292215bd4 | \([1, 0, 1, -5566124, -5054954203]\) | \(10765299591712341649/20708625\) | \(36686592413625\) | \([2]\) | \(5406720\) | \(2.2844\) |
Rank
sage: E.rank()
The elliptic curves in class 292215bd have rank \(0\).
Complex multiplication
The elliptic curves in class 292215bd do not have complex multiplication.Modular form 292215.2.a.bd
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 Cremona 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 Cremona labels.
