Show commands:
SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 52416.ft
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52416.ft1 | 52416ev3 | \([0, 0, 0, -15008556, -22380176432]\) | \(-1956469094246217097/36641439744\) | \(-7002288180003078144\) | \([]\) | \(2985984\) | \(2.7405\) | |
| 52416.ft2 | 52416ev2 | \([0, 0, 0, -69996, -68257712]\) | \(-198461344537/10417365504\) | \(-1990789549894139904\) | \([]\) | \(995328\) | \(2.1912\) | |
| 52416.ft3 | 52416ev1 | \([0, 0, 0, 7764, 2503888]\) | \(270840023/14329224\) | \(-2738357350170624\) | \([]\) | \(331776\) | \(1.6419\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 52416.ft have rank \(1\).
Complex multiplication
The elliptic curves in class 52416.ft do not have complex multiplication.Modular form 52416.2.a.ft
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
