Properties

Label 69360cl
Number of curves $2$
Conductor $69360$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cl1")
 
E.isogeny_class()
 

Elliptic curves in class 69360cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69360.i2 69360cl1 \([0, -1, 0, -70901, -420099]\) \(115220905984/66430125\) \(22725879685632000\) \([]\) \(497664\) \(1.8281\) \(\Gamma_0(N)\)-optimal
69360.i1 69360cl2 \([0, -1, 0, -3816341, 2870834205]\) \(17968412610002944/158203125\) \(54121608000000000\) \([]\) \(1492992\) \(2.3774\)  

Rank

sage: E.rank()
 

The elliptic curves in class 69360cl have rank \(1\).

Complex multiplication

The elliptic curves in class 69360cl do not have complex multiplication.

Modular form 69360.2.a.cl

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} + 3 q^{11} - 4 q^{13} + q^{15} - 5 q^{19} + O(q^{20})\) 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.