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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 250173n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250173.n2 | 250173n1 | \([0, 0, 1, -766764, -258428258]\) | \(39248538107904/71687\) | \(91059607923669\) | \([]\) | \(1866240\) | \(1.9355\) | \(\Gamma_0(N)\)-optimal |
250173.n1 | 250173n2 | \([0, 0, 1, -994194, -92735395]\) | \(117361115136/63905303\) | \(59176571038313259069\) | \([]\) | \(5598720\) | \(2.4848\) |
Rank
sage: E.rank()
The elliptic curves in class 250173n have rank \(1\).
Complex multiplication
The elliptic curves in class 250173n do not have complex multiplication.Modular form 250173.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.