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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 6960.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6960.bd1 | 6960bi2 | \([0, 1, 0, -2096, 36180]\) | \(248739515569/504600\) | \(2066841600\) | \([2]\) | \(4608\) | \(0.67417\) | |
| 6960.bd2 | 6960bi1 | \([0, 1, 0, -176, 84]\) | \(148035889/83520\) | \(342097920\) | \([2]\) | \(2304\) | \(0.32759\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6960.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 6960.bd do not have complex multiplication.Modular form 6960.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
