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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 59840.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59840.bl1 | 59840be1 | \([0, -1, 0, -1765, 28245]\) | \(594160697344/21156245\) | \(21663994880\) | \([2]\) | \(46080\) | \(0.75373\) | \(\Gamma_0(N)\)-optimal |
| 59840.bl2 | 59840be2 | \([0, -1, 0, 655, 97457]\) | \(1893932336/252651025\) | \(-4139434393600\) | \([2]\) | \(92160\) | \(1.1003\) |
Rank
sage: E.rank()
The elliptic curves in class 59840.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 59840.bl do not have complex multiplication.Modular form 59840.2.a.bl
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.
