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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 363726i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363726.i2 | 363726i1 | \([1, -1, 0, 93087, 2820285]\) | \(51895117/32064\) | \(-55116216143119296\) | \([2]\) | \(3345408\) | \(1.9015\) | \(\Gamma_0(N)\)-optimal |
| 363726.i1 | 363726i2 | \([1, -1, 0, -386073, 23232501]\) | \(3702294323/2008008\) | \(3451653035962845912\) | \([2]\) | \(6690816\) | \(2.2481\) |
Rank
sage: E.rank()
The elliptic curves in class 363726i have rank \(1\).
Complex multiplication
The elliptic curves in class 363726i do not have complex multiplication.Modular form 363726.2.a.i
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 Cremona 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 Cremona labels.
