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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 38025db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38025.k1 | 38025db1 | \([0, 0, 1, -141375, -20464844]\) | \(-99897344/27\) | \(-84460060546875\) | \([]\) | \(299520\) | \(1.6555\) | \(\Gamma_0(N)\)-optimal |
| 38025.k2 | 38025db2 | \([0, 0, 1, 882375, 46078906]\) | \(24288219136/14348907\) | \(-44885539037091796875\) | \([]\) | \(1497600\) | \(2.4602\) |
Rank
sage: E.rank()
The elliptic curves in class 38025db have rank \(0\).
Complex multiplication
The elliptic curves in class 38025db do not have complex multiplication.Modular form 38025.2.a.db
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
