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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2394.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2394.f1 | 2394d2 | \([1, -1, 0, -29295, 1562733]\) | \(3814038123905521/773540010432\) | \(563910667604928\) | \([2]\) | \(21504\) | \(1.5462\) | |
2394.f2 | 2394d1 | \([1, -1, 0, -9135, -312147]\) | \(115650783909361/8339853312\) | \(6079753064448\) | \([2]\) | \(10752\) | \(1.1997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2394.f have rank \(0\).
Complex multiplication
The elliptic curves in class 2394.f do not have complex multiplication.Modular form 2394.2.a.f
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.