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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 54208.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54208.t1 | 54208bn2 | \([0, 1, 0, -398977, -89674785]\) | \(15124197817/1294139\) | \(601003440466558976\) | \([2]\) | \(737280\) | \(2.1526\) | |
54208.t2 | 54208bn1 | \([0, 1, 0, 26943, -6450017]\) | \(4657463/41503\) | \(-19274162813796352\) | \([2]\) | \(368640\) | \(1.8061\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54208.t have rank \(1\).
Complex multiplication
The elliptic curves in class 54208.t do not have complex multiplication.Modular form 54208.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.