# Properties

 Label 76230t Number of curves 8 Conductor 76230 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("76230.c1")

sage: E.isogeny_class()

## Elliptic curves in class 76230t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.c7 76230t1 [1, -1, 0, -541800, 153576000] [2] 1105920 $$\Gamma_0(N)$$-optimal
76230.c6 76230t2 [1, -1, 0, -628920, 100938096] [2, 2] 2211840
76230.c5 76230t3 [1, -1, 0, -1603575, -593603235] [2] 3317760
76230.c8 76230t4 [1, -1, 0, 2093580, 739636596] [2] 4423680
76230.c4 76230t5 [1, -1, 0, -4745340, -3907631700] [2] 4423680
76230.c2 76230t6 [1, -1, 0, -23906295, -44980476579] [2, 2] 6635520
76230.c3 76230t7 [1, -1, 0, -22163895, -51816608739] [2] 13271040
76230.c1 76230t8 [1, -1, 0, -382492215, -2879171871075] [2] 13271040

## Rank

sage: E.rank()

The elliptic curves in class 76230t have rank $$1$$.

## Modular form 76230.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 2q^{13} + q^{14} + q^{16} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.