# Properties

 Label 58800.m Number of curves $6$ Conductor $58800$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 58800.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.m1 58800gb6 $$[0, -1, 0, -15366808, -23180759888]$$ $$53297461115137/147$$ $$1106841792000000$$ $$[2]$$ $$1572864$$ $$2.5450$$
58800.m2 58800gb4 $$[0, -1, 0, -960808, -361655888]$$ $$13027640977/21609$$ $$162705743424000000$$ $$[2, 2]$$ $$786432$$ $$2.1985$$
58800.m3 58800gb3 $$[0, -1, 0, -764808, 256136112]$$ $$6570725617/45927$$ $$345808999872000000$$ $$[2]$$ $$786432$$ $$2.1985$$
58800.m4 58800gb5 $$[0, -1, 0, -666808, -587447888]$$ $$-4354703137/17294403$$ $$-130218829987008000000$$ $$[2]$$ $$1572864$$ $$2.5450$$
58800.m5 58800gb2 $$[0, -1, 0, -78808, -1799888]$$ $$7189057/3969$$ $$29884728384000000$$ $$[2, 2]$$ $$393216$$ $$1.8519$$
58800.m6 58800gb1 $$[0, -1, 0, 19192, -231888]$$ $$103823/63$$ $$-474360768000000$$ $$[2]$$ $$196608$$ $$1.5053$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 58800.m have rank $$1$$.

## Complex multiplication

The elliptic curves in class 58800.m do not have complex multiplication.

## Modular form 58800.2.a.m

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.