Properties

Label 101430eh
Number of curves $2$
Conductor $101430$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("eh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 101430eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.dt1 101430eh1 \([1, -1, 1, -10373, 226797]\) \(1439069689/579600\) \(49710043731600\) \([2]\) \(294912\) \(1.3261\) \(\Gamma_0(N)\)-optimal
101430.dt2 101430eh2 \([1, -1, 1, 33727, 1620357]\) \(49471280711/41992020\) \(-3601492668354420\) \([2]\) \(589824\) \(1.6726\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101430eh have rank \(1\).

Complex multiplication

The elliptic curves in class 101430eh do not have complex multiplication.

Modular form 101430.2.a.eh

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 2q^{11} - 4q^{13} + q^{16} - 6q^{17} + 4q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.