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Properties

Label 177450.be
Number of curves $1$
Conductor $177450$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("be1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 177450.be1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(7\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 3 T + 11 T^{2}\) 1.11.ad
\(17\) \( 1 - T + 17 T^{2}\) 1.17.ab
\(19\) \( 1 + 5 T + 19 T^{2}\) 1.19.f
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 - 3 T + 29 T^{2}\) 1.29.ad
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 177450.be do not have complex multiplication.

Modular form 177450.2.a.be

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 3 q^{11} - q^{12} + q^{14} + q^{16} + q^{17} - q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 177450.be

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.be1 177450kc1 \([1, 1, 0, -454275, 117133125]\) \(813420049/4200\) \(53532328565625000\) \([]\) \(2515968\) \(2.0557\) \(\Gamma_0(N)\)-optimal