↑

Properties

Label 35739.d
Number of curves $2$
Conductor $35739$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 35739.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35739.d1 35739d1 \([1, -1, 1, -125, 516]\) \(1157625/121\) \(22408353\) \([2]\) \(8640\) \(0.14540\) \(\Gamma_0(N)\)-optimal
35739.d2 35739d2 \([1, -1, 1, 160, 2340]\) \(2460375/14641\) \(-2711410713\) \([2]\) \(17280\) \(0.49198\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35739.d have rank \(1\).

Complex multiplication

The elliptic curves in class 35739.d do not have complex multiplication.

Modular form 35739.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - 4 q^{7} + 3 q^{8} - q^{11} + 4 q^{13} + 4 q^{14} - q^{16} - 4 q^{17} + O(q^{20})\) Copy content Toggle raw display

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.