Properties

Label 42336.e
Number of curves $1$
Conductor $42336$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 42336.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42336.e1 42336bn1 \([0, 0, 0, -1176, -16464]\) \(-13824\) \(-13011038208\) \([]\) \(31680\) \(0.69035\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42336.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 42336.e do not have complex multiplication.

Modular form 42336.2.a.e

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