Properties

Label 2112b
Number of curves 2
Conductor 2112
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("2112.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2112b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2112.g1 2112b1 [0, -1, 0, -393, -2871] [2] 384 \(\Gamma_0(N)\)-optimal
2112.g2 2112b2 [0, -1, 0, -353, -3519] [2] 768  

Rank

sage: E.rank()
 

The elliptic curves in class 2112b have rank \(1\).

Modular form 2112.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{7} + q^{9} - q^{11} - 4q^{13} - 2q^{17} + O(q^{20}) \)

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 Cremona 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 Cremona labels.