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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 17640.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17640.e1 | 17640v1 | \([0, 0, 0, -413238, -102246487]\) | \(1950665639360512/492075\) | \(1968670040400\) | \([2]\) | \(92160\) | \(1.7340\) | \(\Gamma_0(N)\)-optimal |
| 17640.e2 | 17640v2 | \([0, 0, 0, -411663, -103064542]\) | \(-120527903507632/1937102445\) | \(-123997863696618240\) | \([2]\) | \(184320\) | \(2.0806\) |
Rank
sage: E.rank()
The elliptic curves in class 17640.e have rank \(1\).
Complex multiplication
The elliptic curves in class 17640.e do not have complex multiplication.Modular form 17640.2.a.e
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.
