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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 123840.fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.fv1 | 123840w2 | \([0, 0, 0, -80172, -8737264]\) | \(64413688156056/1155625\) | \(1022423040000\) | \([2]\) | \(262144\) | \(1.4312\) | |
| 123840.fv2 | 123840w1 | \([0, 0, 0, -5172, -127264]\) | \(138348848448/16796875\) | \(1857600000000\) | \([2]\) | \(131072\) | \(1.0847\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 123840.fv have rank \(1\).
Complex multiplication
The elliptic curves in class 123840.fv do not have complex multiplication.Modular form 123840.2.a.fv
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.
