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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 960.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
960.f1 | 960k3 | \([0, -1, 0, -225, -1215]\) | \(38614472/405\) | \(13271040\) | \([2]\) | \(256\) | \(0.18331\) | |
960.f2 | 960k2 | \([0, -1, 0, -25, 25]\) | \(438976/225\) | \(921600\) | \([2, 2]\) | \(128\) | \(-0.16327\) | |
960.f3 | 960k1 | \([0, -1, 0, -20, 42]\) | \(14526784/15\) | \(960\) | \([2]\) | \(64\) | \(-0.50984\) | \(\Gamma_0(N)\)-optimal |
960.f4 | 960k4 | \([0, -1, 0, 95, 97]\) | \(2863288/1875\) | \(-61440000\) | \([4]\) | \(256\) | \(0.18331\) |
Rank
sage: E.rank()
The elliptic curves in class 960.f have rank \(1\).
Complex multiplication
The elliptic curves in class 960.f do not have complex multiplication.Modular form 960.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.