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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 111090l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111090.m1 | 111090l1 | \([1, 1, 0, -1996929252, 34329892004496]\) | \(5949010462538271898545049/3314625947988102720\) | \(490683598912886547578518080\) | \([2]\) | \(112020480\) | \(4.0689\) | \(\Gamma_0(N)\)-optimal |
111090.m2 | 111090l2 | \([1, 1, 0, -1641293132, 46944803071464]\) | \(-3303050039017428591035929/4519896503737558217400\) | \(-669106897118781253402064268600\) | \([2]\) | \(224040960\) | \(4.4155\) |
Rank
sage: E.rank()
The elliptic curves in class 111090l have rank \(1\).
Complex multiplication
The elliptic curves in class 111090l do not have complex multiplication.Modular form 111090.2.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 Cremona 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 Cremona labels.