Properties

Label 3024.p
Number of curves $3$
Conductor $3024$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3024.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3024.p1 3024m3 \([0, 0, 0, -152955, 23024682]\) \(-545407363875/14\) \(-10158317568\) \([]\) \(7776\) \(1.4363\)  
3024.p2 3024m2 \([0, 0, 0, -1755, 36234]\) \(-7414875/2744\) \(-221225582592\) \([]\) \(2592\) \(0.88703\)  
3024.p3 3024m1 \([0, 0, 0, 165, -502]\) \(4492125/3584\) \(-396361728\) \([]\) \(864\) \(0.33772\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3024.p have rank \(0\).

Complex multiplication

The elliptic curves in class 3024.p do not have complex multiplication.

Modular form 3024.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{7} + 5 q^{13} + 3 q^{17} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.