# Properties

 Label 10304.t Number of curves $2$ Conductor $10304$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 10304.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.t1 10304bj2 $$[0, 0, 0, -3916, -94320]$$ $$50668941906/1127$$ $$147718144$$ $$[2]$$ $$4096$$ $$0.68251$$
10304.t2 10304bj1 $$[0, 0, 0, -236, -1584]$$ $$-22180932/3703$$ $$-242679808$$ $$[2]$$ $$2048$$ $$0.33594$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 10304.2.a.t

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 3q^{9} + 4q^{13} - 4q^{17} - 2q^{19} + O(q^{20})$$

## 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.