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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 379050.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 379050.x1 | 379050x2 | \([1, 1, 0, -145650150, 676462792500]\) | \(67772591234011/5715360\) | \(28816818130909147500000\) | \([2]\) | \(78796800\) | \(3.3528\) | |
| 379050.x2 | 379050x1 | \([1, 1, 0, -8470150, 12100052500]\) | \(-13328910811/4838400\) | \(-24395189952092400000000\) | \([2]\) | \(39398400\) | \(3.0062\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 379050.x have rank \(1\).
Complex multiplication
The elliptic curves in class 379050.x do not have complex multiplication.Modular form 379050.2.a.x
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.
