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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 36100.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36100.g1 | 36100g1 | \([0, -1, 0, -8315033, -8604352438]\) | \(5405726654464/407253125\) | \(4789895513907031250000\) | \([2]\) | \(2073600\) | \(2.9053\) | \(\Gamma_0(N)\)-optimal |
| 36100.g2 | 36100g2 | \([0, -1, 0, 7975092, -38219799688]\) | \(298091207216/3525390625\) | \(-663420431289062500000000\) | \([2]\) | \(4147200\) | \(3.2519\) |
Rank
sage: E.rank()
The elliptic curves in class 36100.g have rank \(1\).
Complex multiplication
The elliptic curves in class 36100.g do not have complex multiplication.Modular form 36100.2.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.
