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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 115920.eu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.eu1 | 115920eu2 | \([0, 0, 0, -2247867, -1297041174]\) | \(420676324562824569/56350000000\) | \(168260198400000000\) | \([2]\) | \(2064384\) | \(2.3244\) | |
115920.eu2 | 115920eu1 | \([0, 0, 0, -128187, -23961366]\) | \(-78013216986489/37918720000\) | \(-113224691220480000\) | \([2]\) | \(1032192\) | \(1.9778\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.eu have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.eu do not have complex multiplication.Modular form 115920.2.a.eu
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.