Properties

Label 2475g
Number of curves $4$
Conductor $2475$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2475g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2475.g3 2475g1 \([1, -1, 0, -1467, 21816]\) \(30664297/297\) \(3383015625\) \([2]\) \(1536\) \(0.64825\) \(\Gamma_0(N)\)-optimal
2475.g2 2475g2 \([1, -1, 0, -2592, -15309]\) \(169112377/88209\) \(1004755640625\) \([2, 2]\) \(3072\) \(0.99482\)  
2475.g1 2475g3 \([1, -1, 0, -32967, -2293434]\) \(347873904937/395307\) \(4502793796875\) \([2]\) \(6144\) \(1.3414\)  
2475.g4 2475g4 \([1, -1, 0, 9783, -126684]\) \(9090072503/5845851\) \(-66587896546875\) \([2]\) \(6144\) \(1.3414\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2475g have rank \(0\).

Complex multiplication

The elliptic curves in class 2475g do not have complex multiplication.

Modular form 2475.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 4 q^{7} - 3 q^{8} - q^{11} + 2 q^{13} - 4 q^{14} - q^{16} - 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.