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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 412224l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 412224.l2 | 412224l1 | \([0, -1, 0, -74967073, 249838899361]\) | \(177744208950637895247625/17681950027579392\) | \(4635217108029772136448\) | \([]\) | \(38983680\) | \(3.1919\) | \(\Gamma_0(N)\)-optimal |
| 412224.l1 | 412224l2 | \([0, -1, 0, -161859553, -425884474271]\) | \(1788952473315990499029625/736296634487918297088\) | \(193015744951200854071836672\) | \([]\) | \(116951040\) | \(3.7412\) |
Rank
sage: E.rank()
The elliptic curves in class 412224l have rank \(0\).
Complex multiplication
The elliptic curves in class 412224l do not have complex multiplication.Modular form 412224.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
