Properties

Label 7623m
Number of curves 2
Conductor 7623
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("7623.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7623m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7623.l2 7623m1 [0, 0, 1, -7986, -84186] [] 16896 \(\Gamma_0(N)\)-optimal
7623.l1 7623m2 [0, 0, 1, -367356, 85697433] [3] 50688  

Rank

sage: E.rank()
 

The elliptic curves in class 7623m have rank \(0\).

Modular form 7623.2.a.l

sage: E.q_eigenform(10)
 
\( q - 2q^{4} + 3q^{5} + q^{7} - 4q^{13} + 4q^{16} + 3q^{17} + 2q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.