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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 52800ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52800.et4 | 52800ch1 | \([0, 1, 0, 21867, -4565637]\) | \(72268906496/606436875\) | \(-9702990000000000\) | \([2]\) | \(221184\) | \(1.7490\) | \(\Gamma_0(N)\)-optimal |
| 52800.et3 | 52800ch2 | \([0, 1, 0, -315633, -62953137]\) | \(13584145739344/1195803675\) | \(306125740800000000\) | \([2]\) | \(442368\) | \(2.0955\) | |
| 52800.et2 | 52800ch3 | \([0, 1, 0, -1562133, -752609637]\) | \(-26348629355659264/24169921875\) | \(-386718750000000000\) | \([2]\) | \(663552\) | \(2.2983\) | |
| 52800.et1 | 52800ch4 | \([0, 1, 0, -24999633, -48119797137]\) | \(6749703004355978704/5671875\) | \(1452000000000000\) | \([2]\) | \(1327104\) | \(2.6448\) |
Rank
sage: E.rank()
The elliptic curves in class 52800ch have rank \(0\).
Complex multiplication
The elliptic curves in class 52800ch do not have complex multiplication.Modular form 52800.2.a.ch
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.
