# Properties

 Label 7600.r Number of curves $2$ Conductor $7600$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 7600.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7600.r1 7600q1 $$[0, -1, 0, -23033, -1247188]$$ $$5405726654464/407253125$$ $$101813281250000$$ $$$$ $$23040$$ $$1.4331$$ $$\Gamma_0(N)$$-optimal
7600.r2 7600q2 $$[0, -1, 0, 22092, -5579188]$$ $$298091207216/3525390625$$ $$-14101562500000000$$ $$$$ $$46080$$ $$1.7797$$

## Rank

sage: E.rank()

The elliptic curves in class 7600.r have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7600.r do not have complex multiplication.

## Modular form7600.2.a.r

sage: E.q_eigenform(10)

$$q + 2 q^{3} + 2 q^{7} + q^{9} - 6 q^{13} - 2 q^{17} + q^{19} + O(q^{20})$$

## 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. 