# Properties

 Label 7600.m Number of curves $2$ Conductor $7600$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 7600.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7600.m1 7600k2 $$[0, 1, 0, -1112008, 450975988]$$ $$-2376117230685121/342950$$ $$-21948800000000$$ $$[]$$ $$41472$$ $$1.9690$$
7600.m2 7600k1 $$[0, 1, 0, -12008, 775988]$$ $$-2992209121/2375000$$ $$-152000000000000$$ $$[]$$ $$13824$$ $$1.4197$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7600.m have rank $$0$$.

## Complex multiplication

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

## Modular form7600.2.a.m

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 