Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 361361.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361361.g1 | 361361g3 | \([1, -1, 0, -3579563, 2607607470]\) | \(107818231938348177/4463459\) | \(209987360962379\) | \([2]\) | \(4202496\) | \(2.2344\) | |
| 361361.g2 | 361361g4 | \([1, -1, 0, -363053, -15690724]\) | \(112489728522417/62811265517\) | \(2955011322972185477\) | \([2]\) | \(4202496\) | \(2.2344\) | |
| 361361.g3 | 361361g2 | \([1, -1, 0, -224068, 40653795]\) | \(26444947540257/169338169\) | \(7966663347531889\) | \([2, 2]\) | \(2101248\) | \(1.8879\) | |
| 361361.g4 | 361361g1 | \([1, -1, 0, -5663, 1384576]\) | \(-426957777/17320303\) | \(-814848913821943\) | \([2]\) | \(1050624\) | \(1.5413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 361361.g have rank \(0\).
Complex multiplication
The elliptic curves in class 361361.g do not have complex multiplication.Modular form 361361.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
