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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 10608r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10608.j2 | 10608r1 | \([0, -1, 0, -3153, -67104]\) | \(216727177216000/2738853\) | \(43821648\) | \([2]\) | \(5760\) | \(0.61257\) | \(\Gamma_0(N)\)-optimal |
| 10608.j3 | 10608r2 | \([0, -1, 0, -3068, -70980]\) | \(-12479332642000/1526829993\) | \(-390868478208\) | \([2]\) | \(11520\) | \(0.95915\) | |
| 10608.j1 | 10608r3 | \([0, -1, 0, -4953, 19764]\) | \(840033089536000/477272151837\) | \(7636354429392\) | \([2]\) | \(17280\) | \(1.1619\) | |
| 10608.j4 | 10608r4 | \([0, -1, 0, 19612, 137676]\) | \(3258571509326000/1920843121977\) | \(-491735839226112\) | \([2]\) | \(34560\) | \(1.5085\) |
Rank
sage: E.rank()
The elliptic curves in class 10608r have rank \(1\).
Complex multiplication
The elliptic curves in class 10608r do not have complex multiplication.Modular form 10608.2.a.r
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
