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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 348480n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348480.n1 | 348480n1 | \([0, 0, 0, -223608, -39940648]\) | \(702464/15\) | \(26402977793111040\) | \([2]\) | \(3244032\) | \(1.9401\) | \(\Gamma_0(N)\)-optimal |
348480.n2 | 348480n2 | \([0, 0, 0, 15972, -121110352]\) | \(16/225\) | \(-6336714670346649600\) | \([2]\) | \(6488064\) | \(2.2866\) |
Rank
sage: E.rank()
The elliptic curves in class 348480n have rank \(1\).
Complex multiplication
The elliptic curves in class 348480n do not have complex multiplication.Modular form 348480.2.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.