Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 95550.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95550.z1 | 95550p1 | \([1, 1, 0, -629150, 161632500]\) | \(5138936454608263/861237411840\) | \(4615694254080000000\) | \([2]\) | \(2703360\) | \(2.3024\) | \(\Gamma_0(N)\)-optimal |
| 95550.z2 | 95550p2 | \([1, 1, 0, 1162850, 916064500]\) | \(32447412812909177/86348722636800\) | \(-462775185381600000000\) | \([2]\) | \(5406720\) | \(2.6490\) |
Rank
sage: E.rank()
The elliptic curves in class 95550.z have rank \(0\).
Complex multiplication
The elliptic curves in class 95550.z do not have complex multiplication.Modular form 95550.2.a.z
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.
