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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 94640.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.cr1 | 94640bv2 | \([0, -1, 0, -15210056, 21303561200]\) | \(19683218700810001/1478750000000\) | \(29235789040640000000000\) | \([2]\) | \(9031680\) | \(3.0561\) | |
| 94640.cr2 | 94640bv1 | \([0, -1, 0, -3096136, -1703195664]\) | \(166021325905681/32614400000\) | \(644806571825561600000\) | \([2]\) | \(4515840\) | \(2.7096\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94640.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 94640.cr do not have complex multiplication.Modular form 94640.2.a.cr
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.
