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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 7488bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.v2 | 7488bz1 | \([0, 0, 0, -1548, 35856]\) | \(-2146689/1664\) | \(-317995352064\) | \([]\) | \(5376\) | \(0.90587\) | \(\Gamma_0(N)\)-optimal |
| 7488.v1 | 7488bz2 | \([0, 0, 0, -122508, -18108144]\) | \(-1064019559329/125497034\) | \(-23982856676573184\) | \([]\) | \(37632\) | \(1.8788\) |
Rank
sage: E.rank()
The elliptic curves in class 7488bz have rank \(0\).
Complex multiplication
The elliptic curves in class 7488bz do not have complex multiplication.Modular form 7488.2.a.bz
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
