Properties

Label 392784.m
Number of curves $1$
Conductor $392784$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 392784.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392784.m1 392784m1 \([0, -1, 0, -172776, 27703152]\) \(-2841976245512761/385537536\) \(-77378925625344\) \([]\) \(2643840\) \(1.6834\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 392784.m1 has rank \(1\).

Complex multiplication

The elliptic curves in class 392784.m do not have complex multiplication.

Modular form 392784.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 5 q^{11} - 6 q^{13} + q^{15} + 8 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display