Show commands:
SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 28224.em
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.em1 | 28224x2 | \([0, 0, 0, -3980172, 3170971888]\) | \(-6329617441/279936\) | \(-308397268681239822336\) | \([]\) | \(903168\) | \(2.6965\) | |
| 28224.em2 | 28224x1 | \([0, 0, 0, -28812, -4341008]\) | \(-2401/6\) | \(-6610023762886656\) | \([]\) | \(129024\) | \(1.7235\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28224.em have rank \(0\).
Complex multiplication
The elliptic curves in class 28224.em do not have complex multiplication.Modular form 28224.2.a.em
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
