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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 316239.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 316239.j1 | 316239j1 | \([0, 1, 1, -1080597, 435677240]\) | \(-39728447488/392931\) | \(-1380162064308632451\) | \([3]\) | \(5114880\) | \(2.3002\) | \(\Gamma_0(N)\)-optimal |
| 316239.j2 | 316239j2 | \([0, 1, 1, 3478173, 2286993737]\) | \(1324839698432/1409317371\) | \(-4950198309691459361691\) | \([]\) | \(15344640\) | \(2.8495\) |
Rank
sage: E.rank()
The elliptic curves in class 316239.j have rank \(1\).
Complex multiplication
The elliptic curves in class 316239.j do not have complex multiplication.Modular form 316239.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
