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SageMath
E = EllipticCurve("fr1")
E.isogeny_class()
Elliptic curves in class 28224.fr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.fr1 | 28224e1 | \([0, 0, 0, -292236, 60812528]\) | \(-67645179/8\) | \(-326420926562304\) | \([]\) | \(193536\) | \(1.8105\) | \(\Gamma_0(N)\)-optimal |
| 28224.fr2 | 28224e2 | \([0, 0, 0, 37044, 187738992]\) | \(189/512\) | \(-15229494749690855424\) | \([]\) | \(580608\) | \(2.3598\) |
Rank
sage: E.rank()
The elliptic curves in class 28224.fr have rank \(1\).
Complex multiplication
The elliptic curves in class 28224.fr do not have complex multiplication.Modular form 28224.2.a.fr
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.
