Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10304.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.bd1 10304n2 \([0, -1, 0, -67873, 1014945]\) \(263822189935250/149429406721\) \(19586011197734912\) \([2]\) \(61440\) \(1.8161\)  
10304.bd2 10304n1 \([0, -1, 0, 16767, 117761]\) \(7953970437500/4703287687\) \(-308234661855232\) \([2]\) \(30720\) \(1.4695\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 10304.2.a.bd

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{7} + q^{9} - 6q^{17} - 6q^{19} + O(q^{20})\)  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.