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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 2175.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2175.j1 2175f1 \([0, -1, 1, -17458, -882057]\) \(-301302001664/87\) \(-169921875\) \([]\) \(4560\) \(0.94602\) \(\Gamma_0(N)\)-optimal
2175.j2 2175f2 \([0, -1, 1, 28792, -4368307]\) \(1351431663616/4984209207\) \(-9734783607421875\) \([]\) \(22800\) \(1.7507\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2175.2.a.j

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} + q^{9} - 3 q^{11} - 2 q^{12} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 8 q^{17} + 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.