Properties

Label 3675.o
Number of curves $1$
Conductor $3675$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3675.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3675.o1 3675c1 \([0, -1, 1, -7758, 436043]\) \(-1376628736/1366875\) \(-51279169921875\) \([]\) \(16128\) \(1.3265\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3675.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3675.o do not have complex multiplication.

Modular form 3675.2.a.o

sage: E.q_eigenform(10)
 
\(q + 2q^{2} - q^{3} + 2q^{4} - 2q^{6} + q^{9} - 6q^{11} - 2q^{12} + 3q^{13} - 4q^{16} + 4q^{17} + 2q^{18} + q^{19} + O(q^{20})\)  Toggle raw display