↑

Properties

Label 124950.gz
Number of curves $2$
Conductor $124950$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("gz1")
 
E.isogeny_class()
 

Elliptic curves in class 124950.gz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.gz1 124950in2 \([1, 0, 0, -66208213, -197713298833]\) \(17460273607244690041/918397653311250\) \(1688258836162738300781250\) \([2]\) \(35389440\) \(3.4059\)  
124950.gz2 124950in1 \([1, 0, 0, 2698037, -12286580083]\) \(1181569139409959/36161310937500\) \(-66474094851342773437500\) \([2]\) \(17694720\) \(3.0593\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 124950.gz have rank \(1\).

Complex multiplication

The elliptic curves in class 124950.gz do not have complex multiplication.

Modular form 124950.2.a.gz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 6 q^{11} + q^{12} + q^{16} + q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.