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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 35490d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35490.c2 | 35490d1 | \([1, 1, 0, -103743, -11006523]\) | \(56205213778689877/8892231425280\) | \(19536232441340160\) | \([2]\) | \(276480\) | \(1.8486\) | \(\Gamma_0(N)\)-optimal |
35490.c1 | 35490d2 | \([1, 1, 0, -460463, 109493493]\) | \(4914500062643077717/478386819817200\) | \(1051015843138388400\) | \([2]\) | \(552960\) | \(2.1952\) |
Rank
sage: E.rank()
The elliptic curves in class 35490d have rank \(0\).
Complex multiplication
The elliptic curves in class 35490d do not have complex multiplication.Modular form 35490.2.a.d
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.