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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 29040.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29040.t1 | 29040ca2 | \([0, -1, 0, -27817456, 41244600256]\) | \(2711280982499089/732421875000\) | \(643076643000000000000000\) | \([]\) | \(3421440\) | \(3.2764\) | |
| 29040.t2 | 29040ca1 | \([0, -1, 0, -9928816, -12034925120]\) | \(123286270205329/43200000\) | \(37930203788083200000\) | \([]\) | \(1140480\) | \(2.7271\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29040.t have rank \(1\).
Complex multiplication
The elliptic curves in class 29040.t do not have complex multiplication.Modular form 29040.2.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 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.
