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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 349830.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 349830.p1 | 349830p2 | \([1, -1, 0, -32022405, -46498725675]\) | \(1032043291880050009/331708628992000\) | \(1167197668735463718912000\) | \([]\) | \(81285120\) | \(3.3216\) | |
| 349830.p2 | 349830p1 | \([1, -1, 0, -28957590, -59970723084]\) | \(763173572128899049/64679680\) | \(227591220463476480\) | \([]\) | \(27095040\) | \(2.7723\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 349830.p have rank \(1\).
Complex multiplication
The elliptic curves in class 349830.p do not have complex multiplication.Modular form 349830.2.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.
