# Properties

 Label 77315g Number of curves $2$ Conductor $77315$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 77315g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
77315.g2 77315g1 $$[1, -1, 0, -188179, 64550328]$$ $$-658503/1225$$ $$-1370934829550889575$$ $$[2]$$ $$1064832$$ $$2.1701$$ $$\Gamma_0(N)$$-optimal
77315.g1 77315g2 $$[1, -1, 0, -3821984, 2874935115]$$ $$5517084663/4375$$ $$4896195819824605625$$ $$[2]$$ $$2129664$$ $$2.5167$$

## Rank

sage: E.rank()

The elliptic curves in class 77315g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 77315g do not have complex multiplication.

## Modular form 77315.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{5} + q^{7} - 3q^{8} - 3q^{9} + q^{10} + 6q^{11} - 2q^{13} + q^{14} - q^{16} - 2q^{17} - 3q^{18} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.