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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 33810da
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33810.cs1 | 33810da1 | \([1, 0, 0, -12006, -484380]\) | \(1626794704081/83462400\) | \(9819267897600\) | \([2]\) | \(147456\) | \(1.2508\) | \(\Gamma_0(N)\)-optimal |
33810.cs2 | 33810da2 | \([1, 0, 0, 7594, -1907340]\) | \(411664745519/13605414480\) | \(-1600663408157520\) | \([2]\) | \(294912\) | \(1.5974\) |
Rank
sage: E.rank()
The elliptic curves in class 33810da have rank \(1\).
Complex multiplication
The elliptic curves in class 33810da do not have complex multiplication.Modular form 33810.2.a.da
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.