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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 13650.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13650.p1 | 13650t2 | \([1, 1, 0, -10465, 407725]\) | \(1014136091461709/5366088\) | \(670761000\) | \([2]\) | \(18432\) | \(0.88910\) | |
13650.p2 | 13650t1 | \([1, 1, 0, -665, 5925]\) | \(260794641869/17978688\) | \(2247336000\) | \([2]\) | \(9216\) | \(0.54253\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13650.p have rank \(1\).
Complex multiplication
The elliptic curves in class 13650.p do not have complex multiplication.Modular form 13650.2.a.p
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.