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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 160080.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
160080.t1 | 160080cc2 | \([0, -1, 0, -84296, 9339120]\) | \(16172971353271369/215732812500\) | \(883641600000000\) | \([2]\) | \(1179648\) | \(1.6750\) | |
160080.t2 | 160080cc1 | \([0, -1, 0, -776, 385776]\) | \(-12633057289/15667830000\) | \(-64175431680000\) | \([2]\) | \(589824\) | \(1.3284\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 160080.t have rank \(0\).
Complex multiplication
The elliptic curves in class 160080.t do not have complex multiplication.Modular form 160080.2.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.