Properties

Label 64400a
Number of curves $2$
Conductor $64400$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 64400a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.bf2 64400a1 \([0, 0, 0, -1475, -24750]\) \(-22180932/3703\) \(-59248000000\) \([2]\) \(32768\) \(0.79409\) \(\Gamma_0(N)\)-optimal
64400.bf1 64400a2 \([0, 0, 0, -24475, -1473750]\) \(50668941906/1127\) \(36064000000\) \([2]\) \(65536\) \(1.1407\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64400a have rank \(1\).

Complex multiplication

The elliptic curves in class 64400a do not have complex multiplication.

Modular form 64400.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3 q^{9} + 4 q^{13} + 4 q^{17} + 2 q^{19} + O(q^{20})\) 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 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.