Properties

Label 1935.b
Number of curves $2$
Conductor $1935$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 1935.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1935.b1 1935b2 \([1, -1, 1, -83, -268]\) \(2315685267/9245\) \(249615\) \([2]\) \(256\) \(-0.10759\)  
1935.b2 1935b1 \([1, -1, 1, -8, 2]\) \(1860867/1075\) \(29025\) \([2]\) \(128\) \(-0.45417\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1935.b have rank \(1\).

Complex multiplication

The elliptic curves in class 1935.b do not have complex multiplication.

Modular form 1935.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} - 4 q^{7} + 3 q^{8} + q^{10} + 2 q^{13} + 4 q^{14} - q^{16} - 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.