# Properties

 Label 10304.g Number of curves $2$ Conductor $10304$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 10304.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.g1 10304u2 $$[0, 1, 0, -67873, -1014945]$$ $$263822189935250/149429406721$$ $$19586011197734912$$ $$$$ $$61440$$ $$1.8161$$
10304.g2 10304u1 $$[0, 1, 0, 16767, -117761]$$ $$7953970437500/4703287687$$ $$-308234661855232$$ $$$$ $$30720$$ $$1.4695$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10304.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 10304.g do not have complex multiplication.

## Modular form 10304.2.a.g

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{7} + q^{9} - 6q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 