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SageMath
E = EllipticCurve("lm1")
E.isogeny_class()
Elliptic curves in class 242550lm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 242550.lm1 | 242550lm1 | \([1, -1, 1, -2896130, -1895936003]\) | \(74246873427/16940\) | \(612932944109062500\) | \([2]\) | \(7077888\) | \(2.4049\) | \(\Gamma_0(N)\)-optimal |
| 242550.lm2 | 242550lm2 | \([1, -1, 1, -2565380, -2345756003]\) | \(-51603494067/35870450\) | \(-1297885509150939843750\) | \([2]\) | \(14155776\) | \(2.7514\) |
Rank
sage: E.rank()
The elliptic curves in class 242550lm have rank \(0\).
Complex multiplication
The elliptic curves in class 242550lm do not have complex multiplication.Modular form 242550.2.a.lm
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
