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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 147735.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
147735.t1 | 147735y2 | \([0, 0, 1, -1323588, -647374856]\) | \(-2989967081734144/380653171875\) | \(-32647145998065046875\) | \([]\) | \(4147200\) | \(2.4782\) | |
147735.t2 | 147735y1 | \([0, 0, 1, 105252, 1997203]\) | \(1503484706816/890163675\) | \(-76345885459854675\) | \([]\) | \(1382400\) | \(1.9289\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 147735.t have rank \(0\).
Complex multiplication
The elliptic curves in class 147735.t do not have complex multiplication.Modular form 147735.2.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.