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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 481338.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
481338.t1 | 481338t1 | \([1, -1, 0, -3289347, -2087747051]\) | \(3047678972871625/304559880768\) | \(393329330654331120192\) | \([2]\) | \(20643840\) | \(2.6881\) | \(\Gamma_0(N)\)-optimal |
481338.t2 | 481338t2 | \([1, -1, 0, 4072293, -10110462323]\) | \(5783051584712375/37533175779528\) | \(-48472894294107017938632\) | \([2]\) | \(41287680\) | \(3.0347\) |
Rank
sage: E.rank()
The elliptic curves in class 481338.t have rank \(1\).
Complex multiplication
The elliptic curves in class 481338.t do not have complex multiplication.Modular form 481338.2.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.