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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 65520.ea
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65520.ea1 | 65520bq1 | \([0, 0, 0, -121707, 16342506]\) | \(267080942160036/1990625\) | \(1485993600000\) | \([2]\) | \(286720\) | \(1.5116\) | \(\Gamma_0(N)\)-optimal |
65520.ea2 | 65520bq2 | \([0, 0, 0, -119187, 17051634]\) | \(-125415986034978/11552734375\) | \(-17248140000000000\) | \([2]\) | \(573440\) | \(1.8581\) |
Rank
sage: E.rank()
The elliptic curves in class 65520.ea have rank \(1\).
Complex multiplication
The elliptic curves in class 65520.ea do not have complex multiplication.Modular form 65520.2.a.ea
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.