Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 202860.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202860.c1 | 202860bd1 | \([0, 0, 0, -4454688, 3618670237]\) | \(7124261256822784/475453125\) | \(652444323977250000\) | \([2]\) | \(6635520\) | \(2.4739\) | \(\Gamma_0(N)\)-optimal |
| 202860.c2 | 202860bd2 | \([0, 0, 0, -4179063, 4085964862]\) | \(-367624742361424/115740505125\) | \(-2541213226790878752000\) | \([2]\) | \(13271040\) | \(2.8204\) |
Rank
sage: E.rank()
The elliptic curves in class 202860.c have rank \(1\).
Complex multiplication
The elliptic curves in class 202860.c do not have complex multiplication.Modular form 202860.2.a.c
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.
