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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 350056e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350056.e1 | 350056e1 | \([0, 1, 0, -4132, -48000]\) | \(259108432/118769\) | \(3577101844736\) | \([2]\) | \(473088\) | \(1.1037\) | \(\Gamma_0(N)\)-optimal |
350056.e2 | 350056e2 | \([0, 1, 0, 14488, -345920]\) | \(2791456412/2056579\) | \(-247761369877504\) | \([2]\) | \(946176\) | \(1.4502\) |
Rank
sage: E.rank()
The elliptic curves in class 350056e have rank \(1\).
Complex multiplication
The elliptic curves in class 350056e do not have complex multiplication.Modular form 350056.2.a.e
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 Cremona 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 Cremona labels.