Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 430950.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.n1 | 430950n4 | \([1, 1, 0, -56492075, -85141605375]\) | \(4646502864838966769/1959546071236428\) | \(8408442809582875617187500\) | \([2]\) | \(84480000\) | \(3.4795\) | |
430950.n2 | 430950n3 | \([1, 1, 0, -48594575, -130354792875]\) | \(2957515264288122929/1341458175888\) | \(5756217993019406250000\) | \([2]\) | \(42240000\) | \(3.1329\) | |
430950.n3 | 430950n2 | \([1, 1, 0, -26624575, 52866557125]\) | \(486420302677676849/887808\) | \(3809598000000000\) | \([2]\) | \(16896000\) | \(2.6747\) | \(\Gamma_0(N)\)-optimal* |
430950.n4 | 430950n1 | \([1, 1, 0, -1664575, 824957125]\) | \(118870510293809/160432128\) | \(688416768000000000\) | \([2]\) | \(8448000\) | \(2.3282\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950.n have rank \(0\).
Complex multiplication
The elliptic curves in class 430950.n do not have complex multiplication.Modular form 430950.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.