Properties

Label 198744dh
Number of curves 11
Conductor 198744198744
CM no
Rank 22

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Show commands: SageMath
E = EllipticCurve("dh1")
 
E.isogeny_class()
 

Elliptic curves in class 198744dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
198744.e1 198744dh1 [0,1,0,394728,96644484][0, -1, 0, 394728, -96644484] 69212/8169212/81 7960127683777790976-7960127683777790976 [][] 38338563833856 2.31302.3130 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 198744dh1 has rank 22.

Complex multiplication

The elliptic curves in class 198744dh do not have complex multiplication.

Modular form 198744.2.a.dh

sage: E.q_eigenform(10)
 
qq33q5+q9+3q15+q17+O(q20)q - q^{3} - 3 q^{5} + q^{9} + 3 q^{15} + q^{17} + O(q^{20}) Copy content Toggle raw display