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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8880f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8880.x3 | 8880f1 | \([0, 1, 0, -556, -5236]\) | \(74385620944/1665\) | \(426240\) | \([2]\) | \(4352\) | \(0.19483\) | \(\Gamma_0(N)\)-optimal |
8880.x2 | 8880f2 | \([0, 1, 0, -576, -4860]\) | \(20674973956/2772225\) | \(2838758400\) | \([2, 2]\) | \(8704\) | \(0.54140\) | |
8880.x1 | 8880f3 | \([0, 1, 0, -2376, 39060]\) | \(724629215378/84337245\) | \(172722677760\) | \([2]\) | \(17408\) | \(0.88798\) | |
8880.x4 | 8880f4 | \([0, 1, 0, 904, -24396]\) | \(39849102862/151723125\) | \(-310728960000\) | \([2]\) | \(17408\) | \(0.88798\) |
Rank
sage: E.rank()
The elliptic curves in class 8880f have rank \(0\).
Complex multiplication
The elliptic curves in class 8880f do not have complex multiplication.Modular form 8880.2.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 Cremona 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 Cremona labels.