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SageMath
E = EllipticCurve("oz1")
E.isogeny_class()
Elliptic curves in class 310464.oz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.oz1 | 310464oz1 | \([0, 0, 0, -260484, -51170112]\) | \(150229394496/1331\) | \(17317691854848\) | \([2]\) | \(1179648\) | \(1.7064\) | \(\Gamma_0(N)\)-optimal |
| 310464.oz2 | 310464oz2 | \([0, 0, 0, -254604, -53590320]\) | \(-17535471192/1771561\) | \(-184398782870421504\) | \([2]\) | \(2359296\) | \(2.0530\) |
Rank
sage: E.rank()
The elliptic curves in class 310464.oz have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.oz do not have complex multiplication.Modular form 310464.2.a.oz
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.
