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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 110946.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110946.j1 | 110946i1 | \([1, 1, 0, -1276754, 423300660]\) | \(48455467135993/11704467456\) | \(55597440501392080896\) | \([2]\) | \(3870720\) | \(2.4997\) | \(\Gamma_0(N)\)-optimal |
| 110946.j2 | 110946i2 | \([1, 1, 0, 3026606, 2668793908]\) | \(645487763368967/1020688998912\) | \(-4848379142473935585792\) | \([2]\) | \(7741440\) | \(2.8463\) |
Rank
sage: E.rank()
The elliptic curves in class 110946.j have rank \(0\).
Complex multiplication
The elliptic curves in class 110946.j do not have complex multiplication.Modular form 110946.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
