Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2904.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2904.i1 | 2904n3 | \([0, 1, 0, -85224, -9604608]\) | \(37736227588/33\) | \(59864589312\) | \([2]\) | \(11520\) | \(1.3683\) | |
2904.i2 | 2904n4 | \([0, 1, 0, -12624, 332880]\) | \(122657188/43923\) | \(79679768374272\) | \([2]\) | \(11520\) | \(1.3683\) | |
2904.i3 | 2904n2 | \([0, 1, 0, -5364, -149184]\) | \(37642192/1089\) | \(493882861824\) | \([2, 2]\) | \(5760\) | \(1.0217\) | |
2904.i4 | 2904n1 | \([0, 1, 0, 81, -7614]\) | \(2048/891\) | \(-25255373616\) | \([4]\) | \(2880\) | \(0.67512\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2904.i have rank \(0\).
Complex multiplication
The elliptic curves in class 2904.i do not have complex multiplication.Modular form 2904.2.a.i
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.