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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 86394.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 86394.g1 | 86394g1 | \([1, 1, 0, -2436051, 1461853485]\) | \(1201171623659064689507/552066685599744\) | \(734800758533259264\) | \([2]\) | \(2096640\) | \(2.3851\) | \(\Gamma_0(N)\)-optimal |
| 86394.g2 | 86394g2 | \([1, 1, 0, -2041811, 1951263021]\) | \(-707282001539844916067/827540182872603648\) | \(-1101455983403435455488\) | \([2]\) | \(4193280\) | \(2.7316\) |
Rank
sage: E.rank()
The elliptic curves in class 86394.g have rank \(0\).
Complex multiplication
The elliptic curves in class 86394.g do not have complex multiplication.Modular form 86394.2.a.g
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.
