Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 74704.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74704.n1 | 74704s4 | \([0, 0, 0, -184867499, -967473242150]\) | \(170586815436843383543017473/2166416\) | \(8873639936\) | \([2]\) | \(3686400\) | \(2.8954\) | |
| 74704.n2 | 74704s3 | \([0, 0, 0, -11583659, -15035861542]\) | \(41966336340198080824833/442001722607124848\) | \(1810439055798783377408\) | \([4]\) | \(3686400\) | \(2.8954\) | |
| 74704.n3 | 74704s2 | \([0, 0, 0, -11554219, -15116768550]\) | \(41647175116728660507393/4693358285056\) | \(19223995535589376\) | \([2, 2]\) | \(1843200\) | \(2.5488\) | |
| 74704.n4 | 74704s1 | \([0, 0, 0, -720299, -237462822]\) | \(-10090256344188054273/107965577101312\) | \(-442227003806973952\) | \([2]\) | \(921600\) | \(2.2022\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74704.n have rank \(0\).
Complex multiplication
The elliptic curves in class 74704.n do not have complex multiplication.Modular form 74704.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
