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SageMath
E = EllipticCurve("ns1")
E.isogeny_class()
Elliptic curves in class 348480ns
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.ns2 | 348480ns1 | \([0, 0, 0, -1150347, -452731664]\) | \(2036792051776/107421875\) | \(8878842286875000000\) | \([2]\) | \(5529600\) | \(2.3928\) | \(\Gamma_0(N)\)-optimal |
| 348480.ns1 | 348480ns2 | \([0, 0, 0, -18165972, -29801281664]\) | \(125330290485184/378125\) | \(2000225590387200000\) | \([2]\) | \(11059200\) | \(2.7394\) |
Rank
sage: E.rank()
The elliptic curves in class 348480ns have rank \(1\).
Complex multiplication
The elliptic curves in class 348480ns do not have complex multiplication.Modular form 348480.2.a.ns
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.
