# Properties

 Label 2352v Number of curves 6 Conductor 2352 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2352.v1")

sage: E.isogeny_class()

## Elliptic curves in class 2352v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2352.v6 2352v1 [0, 1, 0, 768, -1548] [2] 1536 $$\Gamma_0(N)$$-optimal
2352.v5 2352v2 [0, 1, 0, -3152, -15660] [2, 2] 3072
2352.v2 2352v3 [0, 1, 0, -38432, -2908620] [2, 2] 6144
2352.v3 2352v4 [0, 1, 0, -30592, 2036852] [4] 6144
2352.v1 2352v5 [0, 1, 0, -614672, -185691948] [2] 12288
2352.v4 2352v6 [0, 1, 0, -26672, -4710252] [2] 12288

## Rank

sage: E.rank()

The elliptic curves in class 2352v have rank $$0$$.

## Modular form2352.2.a.v

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{9} - 4q^{11} + 2q^{13} + 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.