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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 290400.ei
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290400.ei1 | 290400ei2 | \([0, 1, 0, -5848, -167092]\) | \(195112/9\) | \(1020419136000\) | \([2]\) | \(414720\) | \(1.0658\) | |
290400.ei2 | 290400ei1 | \([0, 1, 0, 202, -9792]\) | \(64/3\) | \(-42517464000\) | \([2]\) | \(207360\) | \(0.71919\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 290400.ei have rank \(0\).
Complex multiplication
The elliptic curves in class 290400.ei do not have complex multiplication.Modular form 290400.2.a.ei
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.