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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 25200.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.bc1 | 25200f2 | \([0, 0, 0, -60364575, -180515027250]\) | \(308971819397054448/6565234375\) | \(516894032812500000000\) | \([2]\) | \(2211840\) | \(3.0920\) | |
| 25200.bc2 | 25200f1 | \([0, 0, 0, -3640950, -3026804625]\) | \(-1084767227025408/176547030625\) | \(-868743800947968750000\) | \([2]\) | \(1105920\) | \(2.7454\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25200.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 25200.bc do not have complex multiplication.Modular form 25200.2.a.bc
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.
