# Properties

 Label 7600m Number of curves $3$ 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 7600m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7600.c3 7600m1 $$[0, 1, 0, 267, 163]$$ $$32768/19$$ $$-1216000000$$ $$[]$$ $$2592$$ $$0.43269$$ $$\Gamma_0(N)$$-optimal
7600.c2 7600m2 $$[0, 1, 0, -3733, 92163]$$ $$-89915392/6859$$ $$-438976000000$$ $$[]$$ $$7776$$ $$0.98200$$
7600.c1 7600m3 $$[0, 1, 0, -307733, 65604163]$$ $$-50357871050752/19$$ $$-1216000000$$ $$[]$$ $$23328$$ $$1.5313$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7600.2.a.m

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{7} + q^{9} - 3q^{11} + 4q^{13} + 3q^{17} - q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.