Properties

Label 21675v
Number of curves $1$
Conductor $21675$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 21675v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21675.o1 21675v1 \([0, 1, 1, 4817, 118744]\) \(819200/867\) \(-13079545201875\) \([]\) \(27648\) \(1.2035\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 21675v1 has rank \(1\).

Complex multiplication

The elliptic curves in class 21675v do not have complex multiplication.

Modular form 21675.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{7} + q^{9} - 2 q^{11} - 2 q^{12} + q^{13} + 4 q^{16} - q^{19} + O(q^{20})\) Copy content Toggle raw display