# Properties

 Label 207368.g Number of curves $2$ Conductor $207368$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 207368.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
207368.g1 207368q2 $$[0, 1, 0, -12658088, 17328498592]$$ $$12576878500/1127$$ $$20099216529091632128$$ $$$$ $$8110080$$ $$2.7439$$
207368.g2 207368q1 $$[0, 1, 0, -734428, 311051040]$$ $$-9826000/3703$$ $$-16510070720325269248$$ $$$$ $$4055040$$ $$2.3974$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 207368.g have rank $$1$$.

## Complex multiplication

The elliptic curves in class 207368.g do not have complex multiplication.

## Modular form 207368.2.a.g

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 