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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 223080.dp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 223080.dp1 | 223080bx1 | \([0, 1, 0, -22195, 1261898]\) | \(15657723904/49005\) | \(3784604400720\) | \([2]\) | \(552960\) | \(1.2809\) | \(\Gamma_0(N)\)-optimal |
| 223080.dp2 | 223080bx2 | \([0, 1, 0, -12900, 2336400]\) | \(-192143824/1804275\) | \(-2229476046969600\) | \([2]\) | \(1105920\) | \(1.6275\) |
Rank
sage: E.rank()
The elliptic curves in class 223080.dp have rank \(0\).
Complex multiplication
The elliptic curves in class 223080.dp do not have complex multiplication.Modular form 223080.2.a.dp
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.
