Properties

Label 310464.pc
Number of curves $4$
Conductor $310464$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("pc1")
 
E.isogeny_class()
 

Elliptic curves in class 310464.pc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310464.pc1 310464pc4 \([0, 0, 0, -6393324, -6219544912]\) \(1285429208617/614922\) \(13825336844631932928\) \([2]\) \(9437184\) \(2.6276\)  
310464.pc2 310464pc3 \([0, 0, 0, -3570924, 2554054832]\) \(223980311017/4278582\) \(96195675821289504768\) \([2]\) \(9437184\) \(2.6276\)  
310464.pc3 310464pc2 \([0, 0, 0, -466284, -62535760]\) \(498677257/213444\) \(4798877251855712256\) \([2, 2]\) \(4718592\) \(2.2811\)  
310464.pc4 310464pc1 \([0, 0, 0, 98196, -7216720]\) \(4657463/3696\) \(-83097441590575104\) \([2]\) \(2359296\) \(1.9345\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 310464.pc have rank \(0\).

Complex multiplication

The elliptic curves in class 310464.pc do not have complex multiplication.

Modular form 310464.2.a.pc

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + q^{11} + 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.