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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 241200.dp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 241200.dp1 | 241200dp2 | \([0, 0, 0, -62175, -2983750]\) | \(9115564624/3956283\) | \(11536521228000000\) | \([2]\) | \(1075200\) | \(1.7782\) | |
| 241200.dp2 | 241200dp1 | \([0, 0, 0, 13200, -345625]\) | \(1395654656/1090827\) | \(-198803220750000\) | \([2]\) | \(537600\) | \(1.4316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 241200.dp have rank \(1\).
Complex multiplication
The elliptic curves in class 241200.dp do not have complex multiplication.Modular form 241200.2.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.
