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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 352800.ev
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
352800.ev1 | 352800ev1 | \([0, 0, 0, -290325, -59339000]\) | \(31554496/525\) | \(45027213525000000\) | \([2]\) | \(3538944\) | \(1.9940\) | \(\Gamma_0(N)\)-optimal |
352800.ev2 | 352800ev2 | \([0, 0, 0, -14700, -167384000]\) | \(-64/2205\) | \(-12103314995520000000\) | \([2]\) | \(7077888\) | \(2.3406\) |
Rank
sage: E.rank()
The elliptic curves in class 352800.ev have rank \(1\).
Complex multiplication
The elliptic curves in class 352800.ev do not have complex multiplication.Modular form 352800.2.a.ev
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.