# Properties

 Label 301530.cj Number of curves $4$ Conductor $301530$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cj1")

sage: E.isogeny_class()

## Elliptic curves in class 301530.cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301530.cj1 301530cj3 $$[1, 1, 1, -328520, 72233207]$$ $$26487576322129/44531250$$ $$6592223182031250$$ $$$$ $$3153920$$ $$1.9307$$
301530.cj2 301530cj2 $$[1, 1, 1, -26990, 348455]$$ $$14688124849/8122500$$ $$1202421508402500$$ $$[2, 2]$$ $$1576960$$ $$1.5841$$
301530.cj3 301530cj1 $$[1, 1, 1, -16410, -811113]$$ $$3301293169/22800$$ $$3375218269200$$ $$$$ $$788480$$ $$1.2375$$ $$\Gamma_0(N)$$-optimal
301530.cj4 301530cj4 $$[1, 1, 1, 105260, 2887655]$$ $$871257511151/527800050$$ $$-78133349615994450$$ $$$$ $$3153920$$ $$1.9307$$

## Rank

sage: E.rank()

The elliptic curves in class 301530.cj have rank $$1$$.

## Complex multiplication

The elliptic curves in class 301530.cj do not have complex multiplication.

## Modular form 301530.2.a.cj

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + 2q^{13} - q^{15} + q^{16} - 2q^{17} + q^{18} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 