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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 327990.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327990.n1 | 327990n1 | \([1, 0, 1, -8150149, -2926210384]\) | \(100654290922421809/52033093632000\) | \(30950497556090191872000\) | \([2]\) | \(32256000\) | \(3.0076\) | \(\Gamma_0(N)\)-optimal |
| 327990.n2 | 327990n2 | \([1, 0, 1, 30603131, -22721385808]\) | \(5328847957372469711/3458851344000000\) | \(-2057405443283393424000000\) | \([2]\) | \(64512000\) | \(3.3542\) |
Rank
sage: E.rank()
The elliptic curves in class 327990.n have rank \(1\).
Complex multiplication
The elliptic curves in class 327990.n do not have complex multiplication.Modular form 327990.2.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 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.
