Properties

 Label 700.b Number of curves $1$ Conductor $700$ CM no Rank $1$

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

Elliptic curves in class 700.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
700.b1 700d1 [0, 0, 0, 800, 26500] [] 1440 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 700.b1 has rank $$1$$.

Complex multiplication

The elliptic curves in class 700.b do not have complex multiplication.

Modular form700.2.a.b

sage: E.q_eigenform(10)

$$q - 3q^{3} + q^{7} + 6q^{9} - 5q^{11} + 3q^{13} + q^{17} + 6q^{19} + O(q^{20})$$