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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 244758.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
244758.e1 | 244758e2 | \([1, 1, 0, -2570688, 17604675804]\) | \(-39934705050538129/2823126576537804\) | \(-132816476967734918985324\) | \([]\) | \(23115456\) | \(3.1167\) | |
244758.e2 | 244758e1 | \([1, 1, 0, -599628, -180198576]\) | \(-506814405937489/4048994304\) | \(-190488504195661824\) | \([]\) | \(3302208\) | \(2.1437\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244758.e have rank \(0\).
Complex multiplication
The elliptic curves in class 244758.e do not have complex multiplication.Modular form 244758.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.