# Properties

 Label 15600.q Number of curves $2$ Conductor $15600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 15600.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.q1 15600h1 $$[0, -1, 0, -16283, -745938]$$ $$1909913257984/129730653$$ $$32432663250000$$ $$$$ $$38400$$ $$1.3411$$ $$\Gamma_0(N)$$-optimal
15600.q2 15600h2 $$[0, -1, 0, 14092, -3236688]$$ $$77366117936/1172914587$$ $$-4691658348000000$$ $$$$ $$76800$$ $$1.6877$$

## Rank

sage: E.rank()

The elliptic curves in class 15600.q have rank $$0$$.

## Complex multiplication

The elliptic curves in class 15600.q do not have complex multiplication.

## Modular form 15600.2.a.q

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 2q^{11} + q^{13} - 2q^{17} - 8q^{19} + O(q^{20})$$ ## 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 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. 