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SageMath
E = EllipticCurve("ei1")
E.isogeny_class()
Elliptic curves in class 92400.ei
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.ei1 | 92400ct2 | \([0, 1, 0, -11208, 351588]\) | \(77860436/17787\) | \(35574000000000\) | \([2]\) | \(184320\) | \(1.3127\) | |
92400.ei2 | 92400ct1 | \([0, 1, 0, -3708, -83412]\) | \(11279504/693\) | \(346500000000\) | \([2]\) | \(92160\) | \(0.96614\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.ei have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.ei do not have complex multiplication.Modular form 92400.2.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.