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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 377706.ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377706.ch1 | 377706ch5 | \([1, 1, 1, -7257141527, 237952877081573]\) | \(285531136548675601769470657/17941034271597192\) | \(2655916957975357767623688\) | \([2]\) | \(346030080\) | \(4.1469\) | |
| 377706.ch2 | 377706ch3 | \([1, 1, 1, -454434287, 3703013813621]\) | \(70108386184777836280897/552468975892674624\) | \(81785235991191656551580736\) | \([2, 2]\) | \(173015040\) | \(3.8003\) | |
| 377706.ch3 | 377706ch6 | \([1, 1, 1, -154787527, 8513782616069]\) | \(-2770540998624539614657/209924951154647363208\) | \(-31076426767459798894002171912\) | \([2]\) | \(346030080\) | \(4.1469\) | |
| 377706.ch4 | 377706ch2 | \([1, 1, 1, -47993007, -32181549579]\) | \(82582985847542515777/44772582831427584\) | \(6627949102276519536562176\) | \([2, 2]\) | \(86507520\) | \(3.4537\) | |
| 377706.ch5 | 377706ch1 | \([1, 1, 1, -37159087, -87092189707]\) | \(38331145780597164097/55468445663232\) | \(8211320665204743733248\) | \([2]\) | \(43253760\) | \(3.1072\) | \(\Gamma_0(N)\)-optimal |
| 377706.ch6 | 377706ch4 | \([1, 1, 1, 185105553, -252879266187]\) | \(4738217997934888496063/2928751705237796928\) | \(-433560362345143224637948992\) | \([2]\) | \(173015040\) | \(3.8003\) |
Rank
sage: E.rank()
The elliptic curves in class 377706.ch have rank \(1\).
Complex multiplication
The elliptic curves in class 377706.ch do not have complex multiplication.Modular form 377706.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
