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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 1872.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1872.p1 | 1872j2 | \([0, 0, 0, -9099, 333882]\) | \(1033364331/676\) | \(54500179968\) | \([2]\) | \(2304\) | \(0.99980\) | |
| 1872.p2 | 1872j1 | \([0, 0, 0, -459, 7290]\) | \(-132651/208\) | \(-16769286144\) | \([2]\) | \(1152\) | \(0.65322\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1872.p have rank \(0\).
Complex multiplication
The elliptic curves in class 1872.p do not have complex multiplication.Modular form 1872.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
