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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 20230.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20230.e1 | 20230h2 | \([1, 1, 0, -3133777, -2128900651]\) | \(1688258640889/7000000\) | \(14111957303143000000\) | \([]\) | \(528768\) | \(2.5296\) | |
| 20230.e2 | 20230h1 | \([1, 1, 0, -210542, 34877896]\) | \(511981129/34300\) | \(69148590785400700\) | \([]\) | \(176256\) | \(1.9803\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20230.e have rank \(0\).
Complex multiplication
The elliptic curves in class 20230.e do not have complex multiplication.Modular form 20230.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
