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SageMath
sage: E = EllipticCurve("t1")
sage: E.isogeny_class()
Elliptic curves in class 62400.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
62400.t1 | 62400fg4 | [0, -1, 0, -165633, 25903137] | [2] | 589824 | |
62400.t2 | 62400fg2 | [0, -1, 0, -15633, -46863] | [2, 2] | 294912 | |
62400.t3 | 62400fg1 | [0, -1, 0, -11133, -447363] | [2] | 147456 | \(\Gamma_0(N)\)-optimal |
62400.t4 | 62400fg3 | [0, -1, 0, 62367, -436863] | [2] | 589824 |
Rank
sage: E.rank()
The elliptic curves in class 62400.t have rank \(1\).
Complex multiplication
The elliptic curves in class 62400.t do not have complex multiplication.Modular form 62400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.