Properties

Label 7514.i
Number of curves $2$
Conductor $7514$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 7514.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7514.i1 7514i2 \([1, -1, 1, -61467, -6420203]\) \(-1064019559329/125497034\) \(-3029193317470346\) \([]\) \(70560\) \(1.7064\)  
7514.i2 7514i1 \([1, -1, 1, -777, 12937]\) \(-2146689/1664\) \(-40164914816\) \([]\) \(10080\) \(0.73345\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7514.i have rank \(0\).

Complex multiplication

The elliptic curves in class 7514.i do not have complex multiplication.

Modular form 7514.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} + 3 q^{3} + q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} + 6 q^{9} + q^{10} + 2 q^{11} + 3 q^{12} - q^{13} - q^{14} + 3 q^{15} + q^{16} + 6 q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.