# Properties

 Label 7488.cc Number of curves $2$ Conductor $7488$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cc1")

sage: E.isogeny_class()

## Elliptic curves in class 7488.cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.cc1 7488cc1 $$[0, 0, 0, -23448, 1298360]$$ $$1909913257984/129730653$$ $$96843413541888$$ $$$$ $$30720$$ $$1.4323$$ $$\Gamma_0(N)$$-optimal
7488.cc2 7488cc2 $$[0, 0, 0, 20292, 5584880]$$ $$77366117936/1172914587$$ $$-14009216760594432$$ $$$$ $$61440$$ $$1.7788$$

## Rank

sage: E.rank()

The elliptic curves in class 7488.cc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 7488.cc do not have complex multiplication.

## Modular form7488.2.a.cc

sage: E.q_eigenform(10)

$$q + 4 q^{5} + 2 q^{11} + q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})$$

## 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 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. 