Properties

Label 700.f
Number of curves $2$
Conductor $700$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 700.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
700.f1 700e1 \([0, 0, 0, -2000, -34375]\) \(28311552/49\) \(1531250000\) \([2]\) \(360\) \(0.65639\) \(\Gamma_0(N)\)-optimal
700.f2 700e2 \([0, 0, 0, -1375, -56250]\) \(-574992/2401\) \(-1200500000000\) \([2]\) \(720\) \(1.0030\)  

Rank

sage: E.rank()
 

The elliptic curves in class 700.f have rank \(1\).

Complex multiplication

The elliptic curves in class 700.f do not have complex multiplication.

Modular form 700.2.a.f

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