Properties

 Label 90480.u Number of curves $2$ Conductor $90480$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

Elliptic curves in class 90480.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90480.u1 90480z1 $$[0, -1, 0, -13320, -498960]$$ $$63812982460681/10201800960$$ $$41786576732160$$ $$$$ $$184320$$ $$1.3360$$ $$\Gamma_0(N)$$-optimal
90480.u2 90480z2 $$[0, -1, 0, 23800, -2815248]$$ $$363979050334199/1041836936400$$ $$-4267364091494400$$ $$$$ $$368640$$ $$1.6826$$

Rank

sage: E.rank()

The elliptic curves in class 90480.u have rank $$1$$.

Complex multiplication

The elliptic curves in class 90480.u do not have complex multiplication.

Modular form 90480.2.a.u

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + 4 q^{11} - q^{13} - q^{15} - 4 q^{17} + O(q^{20})$$ 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 LMFDB 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 LMFDB labels. 