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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 1850.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1850.p1 | 1850i1 | \([1, 1, 1, -11888, 1187281]\) | \(-19026212425/51868672\) | \(-506530000000000\) | \([]\) | \(9000\) | \(1.5089\) | \(\Gamma_0(N)\)-optimal |
| 1850.p2 | 1850i2 | \([1, 1, 1, 103737, -27025219]\) | \(12642252501575/39728447488\) | \(-387973120000000000\) | \([]\) | \(27000\) | \(2.0582\) |
Rank
sage: E.rank()
The elliptic curves in class 1850.p have rank \(0\).
Complex multiplication
The elliptic curves in class 1850.p do not have complex multiplication.Modular form 1850.2.a.p
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.
