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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 91091l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91091.h1 | 91091l1 | \([0, -1, 1, -739769, -244657008]\) | \(-78843215872/539\) | \(-306081526850099\) | \([]\) | \(691200\) | \(1.9604\) | \(\Gamma_0(N)\)-optimal |
| 91091.h2 | 91091l2 | \([0, -1, 1, -408529, -464558963]\) | \(-13278380032/156590819\) | \(-88923111262017611579\) | \([]\) | \(2073600\) | \(2.5097\) | |
| 91091.h3 | 91091l3 | \([0, -1, 1, 3649161, 12027039702]\) | \(9463555063808/115539436859\) | \(-65611293590358676379219\) | \([]\) | \(6220800\) | \(3.0590\) |
Rank
sage: E.rank()
The elliptic curves in class 91091l have rank \(1\).
Complex multiplication
The elliptic curves in class 91091l do not have complex multiplication.Modular form 91091.2.a.l
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
