Properties

Label 10304.be
Number of curves $2$
Conductor $10304$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10304.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.be1 10304bd2 \([0, -1, 0, -1953, -32575]\) \(12576878500/1127\) \(73859072\) \([2]\) \(5120\) \(0.54982\)  
10304.be2 10304bd1 \([0, -1, 0, -113, -559]\) \(-9826000/3703\) \(-60669952\) \([2]\) \(2560\) \(0.20324\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10304.be have rank \(1\).

Complex multiplication

The elliptic curves in class 10304.be do not have complex multiplication.

Modular form 10304.2.a.be

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{7} + q^{9} + 4q^{11} - 6q^{13} + O(q^{20})\)  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.