Properties

Label 2175.c
Number of curves $2$
Conductor $2175$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 2175.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2175.c1 2175e2 \([1, 1, 1, -243, 1356]\) \(12698260037/7569\) \(946125\) \([2]\) \(384\) \(0.090849\)  
2175.c2 2175e1 \([1, 1, 1, -18, 6]\) \(5177717/2349\) \(293625\) \([2]\) \(192\) \(-0.25572\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2175.c have rank \(1\).

Complex multiplication

The elliptic curves in class 2175.c do not have complex multiplication.

Modular form 2175.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 2 q^{7} + 3 q^{8} + q^{9} + q^{12} - 4 q^{13} - 2 q^{14} - q^{16} - 2 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.