↑

Properties

Label 68970t
Number of curves $2$
Conductor $68970$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 68970t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
68970.y2 68970t1 \([1, 0, 1, 96, -794]\) \(820803071/2770200\) \(-335194200\) \([]\) \(27648\) \(0.31892\) \(\Gamma_0(N)\)-optimal
68970.y1 68970t2 \([1, 0, 1, -894, 25342]\) \(-652007198689/1929093750\) \(-233420343750\) \([]\) \(82944\) \(0.86823\)  

Rank

sage: E.rank()
 

The elliptic curves in class 68970t have rank \(1\).

Complex multiplication

The elliptic curves in class 68970t do not have complex multiplication.

Modular form 68970.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + q^{13} - q^{14} - q^{15} + q^{16} - 3 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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 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.