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Properties

Label 2175.i
Number of curves $2$
Conductor $2175$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 2175.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2175.i1 2175i2 \([1, 0, 1, -6076, 181673]\) \(12698260037/7569\) \(14783203125\) \([2]\) \(1920\) \(0.89557\)  
2175.i2 2175i1 \([1, 0, 1, -451, 1673]\) \(5177717/2349\) \(4587890625\) \([2]\) \(960\) \(0.54899\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2175.i have rank \(0\).

Complex multiplication

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

Modular form 2175.2.a.i

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.