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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 253253n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
253253.n2 | 253253n1 | \([1, 1, 0, 2055, 36656]\) | \(541343375/625807\) | \(-1108655274727\) | \([2]\) | \(307200\) | \(0.99753\) | \(\Gamma_0(N)\)-optimal |
253253.n1 | 253253n2 | \([1, 1, 0, -11860, 334437]\) | \(104154702625/32188247\) | \(57023443043567\) | \([2]\) | \(614400\) | \(1.3441\) |
Rank
sage: E.rank()
The elliptic curves in class 253253n have rank \(1\).
Complex multiplication
The elliptic curves in class 253253n do not have complex multiplication.Modular form 253253.2.a.n
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 Cremona 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 Cremona labels.