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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 305760fo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
305760.fo2 | 305760fo1 | \([0, 1, 0, -3446, -130320]\) | \(-601211584/609375\) | \(-4588311000000\) | \([2]\) | \(691200\) | \(1.1251\) | \(\Gamma_0(N)\)-optimal |
305760.fo1 | 305760fo2 | \([0, 1, 0, -64696, -6353320]\) | \(497169541448/190125\) | \(11452424256000\) | \([2]\) | \(1382400\) | \(1.4717\) |
Rank
sage: E.rank()
The elliptic curves in class 305760fo have rank \(1\).
Complex multiplication
The elliptic curves in class 305760fo do not have complex multiplication.Modular form 305760.2.a.fo
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.