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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 23184.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23184.o1 | 23184bj4 | \([0, 0, 0, -17811, 914706]\) | \(209267191953/55223\) | \(164894994432\) | \([2]\) | \(40960\) | \(1.1368\) | |
| 23184.o2 | 23184bj2 | \([0, 0, 0, -1251, 10530]\) | \(72511713/25921\) | \(77399691264\) | \([2, 2]\) | \(20480\) | \(0.79025\) | |
| 23184.o3 | 23184bj1 | \([0, 0, 0, -531, -4590]\) | \(5545233/161\) | \(480743424\) | \([2]\) | \(10240\) | \(0.44367\) | \(\Gamma_0(N)\)-optimal |
| 23184.o4 | 23184bj3 | \([0, 0, 0, 3789, 74034]\) | \(2014698447/1958887\) | \(-5849205239808\) | \([2]\) | \(40960\) | \(1.1368\) |
Rank
sage: E.rank()
The elliptic curves in class 23184.o have rank \(1\).
Complex multiplication
The elliptic curves in class 23184.o do not have complex multiplication.Modular form 23184.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
