Show commands:
SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 25200.en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.en1 | 25200cv1 | \([0, 0, 0, -915, -10670]\) | \(-30642435/56\) | \(-154828800\) | \([]\) | \(6912\) | \(0.46307\) | \(\Gamma_0(N)\)-optimal |
| 25200.en2 | 25200cv2 | \([0, 0, 0, 1485, -52110]\) | \(179685/686\) | \(-1382659891200\) | \([]\) | \(20736\) | \(1.0124\) |
Rank
sage: E.rank()
The elliptic curves in class 25200.en have rank \(1\).
Complex multiplication
The elliptic curves in class 25200.en do not have complex multiplication.Modular form 25200.2.a.en
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
