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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 91200.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
91200.l1 | 91200ci2 | \([0, -1, 0, -404833, 99277537]\) | \(28662399178/171\) | \(43776000000000\) | \([2]\) | \(696320\) | \(1.8061\) | |
91200.l2 | 91200ci1 | \([0, -1, 0, -24833, 1617537]\) | \(-13231796/1083\) | \(-138624000000000\) | \([2]\) | \(348160\) | \(1.4595\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 91200.l have rank \(1\).
Complex multiplication
The elliptic curves in class 91200.l do not have complex multiplication.Modular form 91200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.