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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 148120.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 148120.x1 | 148120n1 | \([0, 0, 0, -24863, -1387038]\) | \(44851536/4025\) | \(152536180025600\) | \([2]\) | \(337920\) | \(1.4612\) | \(\Gamma_0(N)\)-optimal |
| 148120.x2 | 148120n2 | \([0, 0, 0, 28037, -6497178]\) | \(16078716/129605\) | \(-19646659987297280\) | \([2]\) | \(675840\) | \(1.8078\) |
Rank
sage: E.rank()
The elliptic curves in class 148120.x have rank \(2\).
Complex multiplication
The elliptic curves in class 148120.x do not have complex multiplication.Modular form 148120.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
