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Properties

Label 69366w
Number of curves $2$
Conductor $69366$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 69366w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69366.u2 69366w1 \([1, 0, 0, 430484, 453494672]\) \(8822561460536124355391/93935597925332680704\) \(-93935597925332680704\) \([7]\) \(1893360\) \(2.5135\) \(\Gamma_0(N)\)-optimal
69366.u1 69366w2 \([1, 0, 0, -203025076, -1113860484568]\) \(-925492188434597796818942768449/373958095272087819200664\) \(-373958095272087819200664\) \([]\) \(13253520\) \(3.4864\)  

Rank

sage: E.rank()
 

The elliptic curves in class 69366w have rank \(1\).

Complex multiplication

The elliptic curves in class 69366w do not have complex multiplication.

Modular form 69366.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + q^{14} - q^{15} + q^{16} + 4 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.