# Properties

 Label 5776.m Number of curves $3$ Conductor $5776$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5776.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5776.m1 5776l3 $$[0, 1, 0, -493968, -1075051756]$$ $$-69173457625/2550136832$$ $$-491411185385426911232$$ $$[]$$ $$155520$$ $$2.6505$$
5776.m2 5776l1 $$[0, 1, 0, -89648, 10304852]$$ $$-413493625/152$$ $$-29290389143552$$ $$[]$$ $$17280$$ $$1.5519$$ $$\Gamma_0(N)$$-optimal
5776.m3 5776l2 $$[0, 1, 0, 54752, 39288820]$$ $$94196375/3511808$$ $$-676725150772625408$$ $$[]$$ $$51840$$ $$2.1012$$

## Rank

sage: E.rank()

The elliptic curves in class 5776.m have rank $$1$$.

## Complex multiplication

The elliptic curves in class 5776.m do not have complex multiplication.

## Modular form5776.2.a.m

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} - 2q^{9} + 6q^{11} - 5q^{13} + 3q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 