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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 91035.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91035.q1 | 91035bi4 | \([1, -1, 1, -292667, 61009566]\) | \(157551496201/13125\) | \(230951277388125\) | \([2]\) | \(655360\) | \(1.8000\) | |
| 91035.q2 | 91035bi2 | \([1, -1, 1, -19562, 817224]\) | \(47045881/11025\) | \(193999073006025\) | \([2, 2]\) | \(327680\) | \(1.4534\) | |
| 91035.q3 | 91035bi1 | \([1, -1, 1, -6557, -191964]\) | \(1771561/105\) | \(1847610219105\) | \([2]\) | \(163840\) | \(1.1068\) | \(\Gamma_0(N)\)-optimal |
| 91035.q4 | 91035bi3 | \([1, -1, 1, 45463, 5056854]\) | \(590589719/972405\) | \(-17110718239131405\) | \([2]\) | \(655360\) | \(1.8000\) |
Rank
sage: E.rank()
The elliptic curves in class 91035.q have rank \(1\).
Complex multiplication
The elliptic curves in class 91035.q do not have complex multiplication.Modular form 91035.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
