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SageMath
E = EllipticCurve("jr1")
E.isogeny_class()
Elliptic curves in class 235200.jr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.jr1 | 235200jr1 | \([0, -1, 0, -1177633, -187596863]\) | \(1092727/540\) | \(89255722106880000000\) | \([2]\) | \(6193152\) | \(2.5213\) | \(\Gamma_0(N)\)-optimal |
| 235200.jr2 | 235200jr2 | \([0, -1, 0, 4310367, -1444348863]\) | \(53582633/36450\) | \(-6024761242214400000000\) | \([2]\) | \(12386304\) | \(2.8678\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.jr have rank \(1\).
Complex multiplication
The elliptic curves in class 235200.jr do not have complex multiplication.Modular form 235200.2.a.jr
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.
