# Properties

 Label 304.c Number of curves $3$ Conductor $304$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

## Elliptic curves in class 304.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304.c1 304b3 $$[0, -1, 0, -1368, 157168]$$ $$-69173457625/2550136832$$ $$-10445360463872$$ $$[]$$ $$432$$ $$1.1783$$
304.c2 304b1 $$[0, -1, 0, -248, -1424]$$ $$-413493625/152$$ $$-622592$$ $$[]$$ $$48$$ $$0.079705$$ $$\Gamma_0(N)$$-optimal
304.c3 304b2 $$[0, -1, 0, 152, -5776]$$ $$94196375/3511808$$ $$-14384365568$$ $$[]$$ $$144$$ $$0.62901$$

## Rank

sage: E.rank()

The elliptic curves in class 304.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 304.c do not have complex multiplication.

## Modular form304.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} - 2 q^{9} + 6 q^{11} + 5 q^{13} + 3 q^{17} - q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.