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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 38025.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38025.bo1 | 38025c1 | \([0, 0, 1, -177450, 28904281]\) | \(-303464448/1625\) | \(-3309003826171875\) | \([]\) | \(193536\) | \(1.8225\) | \(\Gamma_0(N)\)-optimal |
| 38025.bo2 | 38025c2 | \([0, 0, 1, 456300, 153858656]\) | \(7077888/10985\) | \(-16306903215528046875\) | \([]\) | \(580608\) | \(2.3718\) |
Rank
sage: E.rank()
The elliptic curves in class 38025.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 38025.bo do not have complex multiplication.Modular form 38025.2.a.bo
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
