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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 57800.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57800.n1 | 57800s4 | \([0, 0, 0, -773075, -261617250]\) | \(132304644/5\) | \(1931005520000000\) | \([2]\) | \(491520\) | \(2.0191\) | |
| 57800.n2 | 57800s2 | \([0, 0, 0, -50575, -3684750]\) | \(148176/25\) | \(2413756900000000\) | \([2, 2]\) | \(245760\) | \(1.6725\) | |
| 57800.n3 | 57800s1 | \([0, 0, 0, -14450, 614125]\) | \(55296/5\) | \(30171961250000\) | \([2]\) | \(122880\) | \(1.3260\) | \(\Gamma_0(N)\)-optimal |
| 57800.n4 | 57800s3 | \([0, 0, 0, 93925, -20880250]\) | \(237276/625\) | \(-241375690000000000\) | \([2]\) | \(491520\) | \(2.0191\) |
Rank
sage: E.rank()
The elliptic curves in class 57800.n have rank \(0\).
Complex multiplication
The elliptic curves in class 57800.n do not have complex multiplication.Modular form 57800.2.a.n
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.
