Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 361920s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.s3 | 361920s1 | \([0, -1, 0, -1516, 23230]\) | \(6024593993536/706875\) | \(45240000\) | \([2]\) | \(184320\) | \(0.49488\) | \(\Gamma_0(N)\)-optimal |
| 361920.s2 | 361920s2 | \([0, -1, 0, -1641, 19305]\) | \(119386201024/31979025\) | \(130986086400\) | \([2, 2]\) | \(368640\) | \(0.84146\) | |
| 361920.s4 | 361920s3 | \([0, -1, 0, 4159, 120225]\) | \(242737073272/335448945\) | \(-10991991029760\) | \([2]\) | \(737280\) | \(1.1880\) | |
| 361920.s1 | 361920s4 | \([0, -1, 0, -9441, -334815]\) | \(2840362499528/137919795\) | \(4519355842560\) | \([2]\) | \(737280\) | \(1.1880\) |
Rank
sage: E.rank()
The elliptic curves in class 361920s have rank \(2\).
Complex multiplication
The elliptic curves in class 361920s do not have complex multiplication.Modular form 361920.2.a.s
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.
