Properties

Label 64400ba
Number of curves $2$
Conductor $64400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.bd2 64400ba1 \([0, 0, 0, -356075, 110932250]\) \(-78013216986489/37918720000\) \(-2426798080000000000\) \([2]\) \(774144\) \(2.2332\) \(\Gamma_0(N)\)-optimal
64400.bd1 64400ba2 \([0, 0, 0, -6244075, 6004820250]\) \(420676324562824569/56350000000\) \(3606400000000000000\) \([2]\) \(1548288\) \(2.5798\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64400ba have rank \(0\).

Complex multiplication

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

Modular form 64400.2.a.ba

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