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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 15246p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15246.n2 | 15246p1 | \([1, -1, 0, -1824642, 181793013012]\) | \(-520203426765625/11054534935707648\) | \(-14276577781657901740326912\) | \([2]\) | \(3993600\) | \(3.5056\) | \(\Gamma_0(N)\)-optimal |
| 15246.n1 | 15246p2 | \([1, -1, 0, -492484482, 4147011443988]\) | \(10228636028672744397625/167006381634183168\) | \(215683392499137436950945792\) | \([2]\) | \(7987200\) | \(3.8522\) |
Rank
sage: E.rank()
The elliptic curves in class 15246p have rank \(0\).
Complex multiplication
The elliptic curves in class 15246p do not have complex multiplication.Modular form 15246.2.a.p
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.
