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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 266616.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266616.bv1 | 266616bv1 | \([0, 0, 0, -3174, -60835]\) | \(55296/7\) | \(447660528336\) | \([2]\) | \(402688\) | \(0.96483\) | \(\Gamma_0(N)\)-optimal |
| 266616.bv2 | 266616bv2 | \([0, 0, 0, 4761, -316342]\) | \(11664/49\) | \(-50137979173632\) | \([2]\) | \(805376\) | \(1.3114\) |
Rank
sage: E.rank()
The elliptic curves in class 266616.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 266616.bv do not have complex multiplication.Modular form 266616.2.a.bv
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.
