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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 119952.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.r1 | 119952gx2 | \([0, 0, 0, -1972299, 1057388794]\) | \(5799070911693913/54760833024\) | \(8012233590580445184\) | \([]\) | \(2488320\) | \(2.4481\) | |
| 119952.r2 | 119952gx1 | \([0, 0, 0, -173019, -26857334]\) | \(3914907891433/135834624\) | \(19874400681590784\) | \([]\) | \(829440\) | \(1.8988\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.r have rank \(1\).
Complex multiplication
The elliptic curves in class 119952.r do not have complex multiplication.Modular form 119952.2.a.r
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.
