Properties

 Label 9660b Number of curves $2$ Conductor $9660$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 9660b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9660.b1 9660b1 $$[0, -1, 0, -10101, 394110]$$ $$7124261256822784/475453125$$ $$7607250000$$ $$$$ $$17280$$ $$0.95160$$ $$\Gamma_0(N)$$-optimal
9660.b2 9660b2 $$[0, -1, 0, -9476, 444360]$$ $$-367624742361424/115740505125$$ $$-29629569312000$$ $$$$ $$34560$$ $$1.2982$$

Rank

sage: E.rank()

The elliptic curves in class 9660b have rank $$1$$.

Complex multiplication

The elliptic curves in class 9660b do not have complex multiplication.

Modular form9660.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} + 4 q^{11} + 6 q^{13} + q^{15} - 6 q^{17} + 6 q^{19} + O(q^{20})$$ Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 