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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 423864.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
423864.p1 | 423864p2 | \([0, 0, 0, -93351, 10975050]\) | \(21882096/7\) | \(28779931563264\) | \([2]\) | \(1612800\) | \(1.5573\) | \(\Gamma_0(N)\)-optimal* |
423864.p2 | 423864p1 | \([0, 0, 0, -5046, 219501]\) | \(-55296/49\) | \(-12591220058928\) | \([2]\) | \(806400\) | \(1.2108\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 423864.p have rank \(0\).
Complex multiplication
The elliptic curves in class 423864.p do not have complex multiplication.Modular form 423864.2.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.