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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 53130.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53130.o1 | 53130o4 | \([1, 1, 0, -282368102, 1826147359716]\) | \(2489835291441984794384387193961/51540814727119050102000\) | \(51540814727119050102000\) | \([2]\) | \(15728640\) | \(3.4770\) | |
| 53130.o2 | 53130o3 | \([1, 1, 0, -74148102, -218673364284]\) | \(45084144943001919556400313961/5438804975056386677898000\) | \(5438804975056386677898000\) | \([2]\) | \(15728640\) | \(3.4770\) | |
| 53130.o3 | 53130o2 | \([1, 1, 0, -18258102, 26448997716]\) | \(673117119492798278553753961/87156122574176964000000\) | \(87156122574176964000000\) | \([2, 2]\) | \(7864320\) | \(3.1304\) | |
| 53130.o4 | 53130o1 | \([1, 1, 0, 1741898, 2164997716]\) | \(584509378849135526246039/2361777264000000000000\) | \(-2361777264000000000000\) | \([2]\) | \(3932160\) | \(2.7838\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53130.o have rank \(1\).
Complex multiplication
The elliptic curves in class 53130.o do not have complex multiplication.Modular form 53130.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
