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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 59290.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59290.l1 | 59290t2 | \([1, 1, 0, -2673563, -1683725567]\) | \(-61834301948881/20\) | \(-683590102580\) | \([]\) | \(852768\) | \(2.0691\) | |
59290.l2 | 59290t1 | \([1, 1, 0, -32463, -2401307]\) | \(-110699281/8000\) | \(-273436041032000\) | \([]\) | \(284256\) | \(1.5198\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59290.l have rank \(1\).
Complex multiplication
The elliptic curves in class 59290.l do not have complex multiplication.Modular form 59290.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.