Properties

Label 1575.f
Number of curves $3$
Conductor $1575$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1575.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1575.f1 1575e3 \([0, 0, 1, -29550, 2045281]\) \(-250523582464/13671875\) \(-155731201171875\) \([]\) \(4320\) \(1.4815\)  
1575.f2 1575e1 \([0, 0, 1, -300, -2219]\) \(-262144/35\) \(-398671875\) \([]\) \(480\) \(0.38287\) \(\Gamma_0(N)\)-optimal
1575.f3 1575e2 \([0, 0, 1, 1950, 5656]\) \(71991296/42875\) \(-488373046875\) \([]\) \(1440\) \(0.93218\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1575.f have rank \(0\).

Complex multiplication

The elliptic curves in class 1575.f do not have complex multiplication.

Modular form 1575.2.a.f

sage: E.q_eigenform(10)
 
\(q - 2q^{4} - q^{7} + 3q^{11} - 5q^{13} + 4q^{16} + 3q^{17} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.