Properties

Label 198744dh
Number of curves $1$
Conductor $198744$
CM no
Rank $2$

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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 \([0, -1, 0, 394728, -96644484]\) \(69212/81\) \(-7960127683777790976\) \([]\) \(3833856\) \(2.3130\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 198744dh1 has rank \(2\).

Complex multiplication

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

Modular form 198744.2.a.dh

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