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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 271440.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271440.l1 | 271440l1 | \([0, 0, 0, -1077705963, -13744402884838]\) | \(-1251701744499641551742491347/13559824919198275993600\) | \(-1499608157463975738684211200\) | \([]\) | \(113218560\) | \(4.0304\) | \(\Gamma_0(N)\)-optimal |
271440.l2 | 271440l2 | \([0, 0, 0, 3579230997, -71436513206502]\) | \(62898697943298124177490037/63744399417968386000000\) | \(-5139173432294898653749248000000\) | \([]\) | \(339655680\) | \(4.5797\) |
Rank
sage: E.rank()
The elliptic curves in class 271440.l have rank \(1\).
Complex multiplication
The elliptic curves in class 271440.l do not have complex multiplication.Modular form 271440.2.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.