Properties

Label 7938.m
Number of curves $2$
Conductor $7938$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 7938.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7938.m1 7938b2 \([1, -1, 0, -4713, 59597]\) \(9074457/4096\) \(5226454388736\) \([]\) \(18144\) \(1.1356\)  
7938.m2 7938b1 \([1, -1, 0, -3978, 97572]\) \(35801587017/16\) \(3111696\) \([3]\) \(6048\) \(0.58631\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7938.m have rank \(1\).

Complex multiplication

The elliptic curves in class 7938.m do not have complex multiplication.

Modular form 7938.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 3 q^{5} - q^{8} - 3 q^{10} - 3 q^{11} - q^{13} + q^{16} + 3 q^{17} - 7 q^{19} + O(q^{20})\) 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.