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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 4290t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4290.q3 | 4290t1 | \([1, 1, 1, -66, -177]\) | \(31824875809/8785920\) | \(8785920\) | \([2]\) | \(1152\) | \(0.039858\) | \(\Gamma_0(N)\)-optimal |
| 4290.q2 | 4290t2 | \([1, 1, 1, -386, 2639]\) | \(6361447449889/294465600\) | \(294465600\) | \([2, 2]\) | \(2304\) | \(0.38643\) | |
| 4290.q1 | 4290t3 | \([1, 1, 1, -6106, 181103]\) | \(25176685646263969/57915000\) | \(57915000\) | \([2]\) | \(4608\) | \(0.73301\) | |
| 4290.q4 | 4290t4 | \([1, 1, 1, 214, 10799]\) | \(1083523132511/50179392120\) | \(-50179392120\) | \([2]\) | \(4608\) | \(0.73301\) |
Rank
sage: E.rank()
The elliptic curves in class 4290t have rank \(1\).
Complex multiplication
The elliptic curves in class 4290t do not have complex multiplication.Modular form 4290.2.a.t
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
