Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 218405c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 218405.c2 | 218405c1 | \([1, 1, 1, -262996, -41180996]\) | \(24137569/5225\) | \(435475785749009225\) | \([2]\) | \(2764800\) | \(2.0985\) | \(\Gamma_0(N)\)-optimal |
| 218405.c1 | 218405c2 | \([1, 1, 1, -1355021, 570789814]\) | \(3301293169/218405\) | \(18202887844308585605\) | \([2]\) | \(5529600\) | \(2.4451\) |
Rank
sage: E.rank()
The elliptic curves in class 218405c have rank \(1\).
Complex multiplication
The elliptic curves in class 218405c do not have complex multiplication.Modular form 218405.2.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 Cremona 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 Cremona labels.
