Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 26010.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26010.n1 | 26010o4 | \([1, -1, 0, -17013195, 27014039325]\) | \(30949975477232209/478125000\) | \(8413225104853125000\) | \([2]\) | \(1769472\) | \(2.7664\) | |
26010.n2 | 26010o2 | \([1, -1, 0, -1095075, 395759061]\) | \(8253429989329/936360000\) | \(16476460045344360000\) | \([2, 2]\) | \(884736\) | \(2.4199\) | |
26010.n3 | 26010o1 | \([1, -1, 0, -262755, -45204075]\) | \(114013572049/15667200\) | \(275684560235827200\) | \([2]\) | \(442368\) | \(2.0733\) | \(\Gamma_0(N)\)-optimal |
26010.n4 | 26010o3 | \([1, -1, 0, 1505925, 1989131661]\) | \(21464092074671/109596256200\) | \(-1928487266007330616200\) | \([2]\) | \(1769472\) | \(2.7664\) |
Rank
sage: E.rank()
The elliptic curves in class 26010.n have rank \(0\).
Complex multiplication
The elliptic curves in class 26010.n do not have complex multiplication.Modular form 26010.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.