Properties

Label 3675.q
Number of curves $2$
Conductor $3675$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3675.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3675.q1 3675q1 \([0, 1, 1, -408, 3119]\) \(-102400/3\) \(-220591875\) \([]\) \(1980\) \(0.37986\) \(\Gamma_0(N)\)-optimal
3675.q2 3675q2 \([0, 1, 1, 2042, -156131]\) \(20480/243\) \(-11167463671875\) \([]\) \(9900\) \(1.1846\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3675.q have rank \(0\).

Complex multiplication

The elliptic curves in class 3675.q do not have complex multiplication.

Modular form 3675.2.a.q

sage: E.q_eigenform(10)
 
\(q + 2q^{2} + q^{3} + 2q^{4} + 2q^{6} + q^{9} + 2q^{11} + 2q^{12} - q^{13} - 4q^{16} - 2q^{17} + 2q^{18} + 5q^{19} + O(q^{20})\)  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.