Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 64400.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.bb1 64400bi1 \([0, 0, 0, -65075, 6387250]\) \(476196576129/197225\) \(12622400000000\) \([2]\) \(221184\) \(1.4758\) \(\Gamma_0(N)\)-optimal
64400.bb2 64400bi2 \([0, 0, 0, -55075, 8417250]\) \(-288673724529/311181605\) \(-19915622720000000\) \([2]\) \(442368\) \(1.8224\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 64400.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3q^{9} - 2q^{11} - 4q^{13} + 6q^{17} + 8q^{19} + O(q^{20})\)  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.