Properties

Label 247962a
Number of curves $2$
Conductor $247962$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 247962a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.a1 247962a1 \([1, 1, 0, -27027, -1229475]\) \(90458382169/25788048\) \(622460787975312\) \([2]\) \(1843200\) \(1.5454\) \(\Gamma_0(N)\)-optimal
247962.a2 247962a2 \([1, 1, 0, 71233, -8009415]\) \(1656015369191/2114999172\) \(-51050938449092868\) \([2]\) \(3686400\) \(1.8919\)  

Rank

sage: E.rank()
 

The elliptic curves in class 247962a have rank \(1\).

Complex multiplication

The elliptic curves in class 247962a do not have complex multiplication.

Modular form 247962.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 4q^{5} + q^{6} - q^{8} + q^{9} + 4q^{10} - q^{11} - q^{12} - q^{13} + 4q^{15} + q^{16} - q^{18} + 2q^{19} + O(q^{20})\)  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.