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Properties

Label 195075.bt
Number of curves $1$
Conductor $195075$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([1, -1, 0, -33867, 680166]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 195075.bt1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1\)
\(5\)\(1\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 - T + 2 T^{2}\) 1.2.ab
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 - 5 T + 11 T^{2}\) 1.11.af
\(13\) \( 1 + 5 T + 13 T^{2}\) 1.13.f
\(19\) \( 1 + 2 T + 19 T^{2}\) 1.19.c
\(23\) \( 1 - 3 T + 23 T^{2}\) 1.23.ad
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 195075.bt do not have complex multiplication.

Modular form 195075.2.a.bt

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3 q^{8} + 5 q^{11} - 5 q^{13} - q^{16} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny graph

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

Elliptic curves in class 195075.bt

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
195075.bt1 195075bs1 \([1, -1, 0, -33867, 680166]\) \(1875\) \(2291183307421875\) \([]\) \(887040\) \(1.6386\) \(\Gamma_0(N)\)-optimal