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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 304920.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304920.ch1 | 304920ch6 | \([0, 0, 0, -11413083, -14840306602]\) | \(62161150998242/1607445\) | \(4251573717871011840\) | \([2]\) | \(10485760\) | \(2.6812\) | |
| 304920.ch2 | 304920ch4 | \([0, 0, 0, -740883, -212989282]\) | \(34008619684/4862025\) | \(6429849141224678400\) | \([2, 2]\) | \(5242880\) | \(2.3346\) | |
| 304920.ch3 | 304920ch2 | \([0, 0, 0, -196383, 30184418]\) | \(2533446736/275625\) | \(91125979892640000\) | \([2, 2]\) | \(2621440\) | \(1.9880\) | |
| 304920.ch4 | 304920ch1 | \([0, 0, 0, -190938, 32113037]\) | \(37256083456/525\) | \(10848330939600\) | \([2]\) | \(1310720\) | \(1.6414\) | \(\Gamma_0(N)\)-optimal |
| 304920.ch5 | 304920ch3 | \([0, 0, 0, 260997, 149926502]\) | \(1486779836/8203125\) | \(-10848330939600000000\) | \([2]\) | \(5242880\) | \(2.3346\) | |
| 304920.ch6 | 304920ch5 | \([0, 0, 0, 1219317, -1148788762]\) | \(75798394558/259416045\) | \(-686136346136909015040\) | \([2]\) | \(10485760\) | \(2.6812\) |
Rank
sage: E.rank()
The elliptic curves in class 304920.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 304920.ch do not have complex multiplication.Modular form 304920.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
