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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 296240bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296240.bt2 | 296240bt1 | \([0, 0, 0, -7534547, -10797701486]\) | \(-78013216986489/37918720000\) | \(-22992205516562759680000\) | \([2]\) | \(17031168\) | \(2.9963\) | \(\Gamma_0(N)\)-optimal |
| 296240.bt1 | 296240bt2 | \([0, 0, 0, -132124627, -584485183854]\) | \(420676324562824569/56350000000\) | \(34168104325734400000000\) | \([2]\) | \(34062336\) | \(3.3428\) |
Rank
sage: E.rank()
The elliptic curves in class 296240bt have rank \(0\).
Complex multiplication
The elliptic curves in class 296240bt do not have complex multiplication.Modular form 296240.2.a.bt
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
