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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 75810c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75810.f2 | 75810c1 | \([1, 1, 0, 1817, 3637]\) | \(96639388469/56448000\) | \(-387176832000\) | \([2]\) | \(134400\) | \(0.91293\) | \(\Gamma_0(N)\)-optimal |
75810.f1 | 75810c2 | \([1, 1, 0, -7303, 20053]\) | \(6281447387851/3601500000\) | \(24702688500000\) | \([2]\) | \(268800\) | \(1.2595\) |
Rank
sage: E.rank()
The elliptic curves in class 75810c have rank \(1\).
Complex multiplication
The elliptic curves in class 75810c do not have complex multiplication.Modular form 75810.2.a.c
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.