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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 57798.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57798.o1 | 57798h3 | \([1, -1, 0, -130077, 145282437]\) | \(-69173457625/2550136832\) | \(-8973278067296305152\) | \([]\) | \(1108080\) | \(2.3170\) | |
| 57798.o2 | 57798h1 | \([1, -1, 0, -23607, -1390635]\) | \(-413493625/152\) | \(-534849051672\) | \([]\) | \(123120\) | \(1.2183\) | \(\Gamma_0(N)\)-optimal |
| 57798.o3 | 57798h2 | \([1, -1, 0, 14418, -5310252]\) | \(94196375/3511808\) | \(-12357152489829888\) | \([]\) | \(369360\) | \(1.7676\) |
Rank
sage: E.rank()
The elliptic curves in class 57798.o have rank \(0\).
Complex multiplication
The elliptic curves in class 57798.o do not have complex multiplication.Modular form 57798.2.a.o
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
