Properties

Label 700.i
Number of curves $2$
Conductor $700$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 700.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
700.i1 700b2 \([0, -1, 0, -98, -343]\) \(-262885120/343\) \(-137200\) \([]\) \(108\) \(-0.10718\)  
700.i2 700b1 \([0, -1, 0, 2, -3]\) \(1280/7\) \(-2800\) \([]\) \(36\) \(-0.65649\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 700.i have rank \(0\).

Complex multiplication

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

Modular form 700.2.a.i

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.