Properties

Label 30960.bz
Number of curves $2$
Conductor $30960$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30960.bz1 30960cc2 [0, 0, 0, -23871747, -44892495614] [2] 1935360  
30960.bz2 30960cc1 [0, 0, 0, -1476867, -716355326] [2] 967680 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.bz have rank \(1\).

Complex multiplication

The elliptic curves in class 30960.bz do not have complex multiplication.

Modular form 30960.2.a.bz

sage: E.q_eigenform(10)
 
\( q + q^{5} + 4q^{7} - 4q^{11} + 4q^{13} - 4q^{17} - 4q^{19} + O(q^{20}) \)

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 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.