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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 141288.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141288.t1 | 141288i3 | \([0, 1, 0, -3391192, 2402550080]\) | \(7080974546692/189\) | \(115119726253056\) | \([2]\) | \(2150400\) | \(2.2118\) | |
| 141288.t2 | 141288i4 | \([0, 1, 0, -329952, -8859312]\) | \(6522128932/3720087\) | \(2265901571838901248\) | \([2]\) | \(2150400\) | \(2.2118\) | |
| 141288.t3 | 141288i2 | \([0, 1, 0, -212212, 37388960]\) | \(6940769488/35721\) | \(5439407065456896\) | \([2, 2]\) | \(1075200\) | \(1.8653\) | |
| 141288.t4 | 141288i1 | \([0, 1, 0, -6167, 1207458]\) | \(-2725888/64827\) | \(-616969782887472\) | \([2]\) | \(537600\) | \(1.5187\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141288.t have rank \(0\).
Complex multiplication
The elliptic curves in class 141288.t do not have complex multiplication.Modular form 141288.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
