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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 6080.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6080.f1 | 6080j1 | \([0, 1, 0, -3685, 79083]\) | \(5405726654464/407253125\) | \(417027200000\) | \([2]\) | \(7680\) | \(0.97495\) | \(\Gamma_0(N)\)-optimal |
6080.f2 | 6080j2 | \([0, 1, 0, 3535, 357775]\) | \(298091207216/3525390625\) | \(-57760000000000\) | \([2]\) | \(15360\) | \(1.3215\) |
Rank
sage: E.rank()
The elliptic curves in class 6080.f have rank \(1\).
Complex multiplication
The elliptic curves in class 6080.f do not have complex multiplication.Modular form 6080.2.a.f
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.