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SageMath
E = EllipticCurve("iv1")
E.isogeny_class()
Elliptic curves in class 242550.iv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.iv1 | 242550iv2 | \([1, -1, 1, -5734280, 5286694347]\) | \(144106117295241933/247808\) | \(35858592000000\) | \([2]\) | \(5046272\) | \(2.2898\) | |
| 242550.iv2 | 242550iv1 | \([1, -1, 1, -358280, 82726347]\) | \(-35148950502093/46137344\) | \(-6676217856000000\) | \([2]\) | \(2523136\) | \(1.9432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 242550.iv have rank \(1\).
Complex multiplication
The elliptic curves in class 242550.iv do not have complex multiplication.Modular form 242550.2.a.iv
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
