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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 63536.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63536.x1 | 63536r1 | \([0, 0, 0, -21299, 1028850]\) | \(5545233/836\) | \(161097140289536\) | \([2]\) | \(172800\) | \(1.4502\) | \(\Gamma_0(N)\)-optimal |
63536.x2 | 63536r2 | \([0, 0, 0, 36461, 5638098]\) | \(27818127/87362\) | \(-16834651160256512\) | \([2]\) | \(345600\) | \(1.7968\) |
Rank
sage: E.rank()
The elliptic curves in class 63536.x have rank \(1\).
Complex multiplication
The elliptic curves in class 63536.x do not have complex multiplication.Modular form 63536.2.a.x
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.