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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 87120.fr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
87120.fr1 | 87120ga1 | \([0, 0, 0, -957, -11869]\) | \(-68679424/3375\) | \(-4763286000\) | \([]\) | \(41472\) | \(0.61857\) | \(\Gamma_0(N)\)-optimal |
87120.fr2 | 87120ga2 | \([0, 0, 0, 4983, -28501]\) | \(9695350016/5859375\) | \(-8269593750000\) | \([]\) | \(124416\) | \(1.1679\) |
Rank
sage: E.rank()
The elliptic curves in class 87120.fr have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.fr do not have complex multiplication.Modular form 87120.2.a.fr
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.