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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 129360.ft
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.ft1 | 129360gy2 | \([0, 1, 0, -11076, -452376]\) | \(1711503051568/7425\) | \(651974400\) | \([2]\) | \(129024\) | \(0.89810\) | |
129360.ft2 | 129360gy1 | \([0, 1, 0, -681, -7470]\) | \(-6373654528/441045\) | \(-2420454960\) | \([2]\) | \(64512\) | \(0.55152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129360.ft have rank \(1\).
Complex multiplication
The elliptic curves in class 129360.ft do not have complex multiplication.Modular form 129360.2.a.ft
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.