Properties

Label 215600.bf
Number of curves $2$
Conductor $215600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 215600.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215600.bf1 215600bd2 \([0, 1, 0, -26172008, -45403544012]\) \(90315183328170247/11712800000000\) \(257119385600000000000000\) \([2]\) \(25952256\) \(3.2205\)  
215600.bf2 215600bd1 \([0, 1, 0, 2499992, -3714456012]\) \(78716413996793/317194240000\) \(-6963047956480000000000\) \([2]\) \(12976128\) \(2.8739\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 215600.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 215600.bf do not have complex multiplication.

Modular form 215600.2.a.bf

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