# Properties

 Label 377520ha Number of curves $6$ Conductor $377520$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("377520.ha1")

sage: E.isogeny_class()

## Elliptic curves in class 377520ha

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
377520.ha6 377520ha1 [0, 1, 0, 29000, 770900] [2] 1966080 $$\Gamma_0(N)$$-optimal
377520.ha5 377520ha2 [0, 1, 0, -125880, 6284628] [2, 2] 3932160
377520.ha2 377520ha3 [0, 1, 0, -1635960, 804210900] [2] 7864320
377520.ha3 377520ha4 [0, 1, 0, -1093880, -436284972] [2, 2] 7864320
377520.ha4 377520ha5 [0, 1, 0, -222680, -1111290732] [2] 15728640
377520.ha1 377520ha6 [0, 1, 0, -17453080, -28070245612] [2] 15728640

## Rank

sage: E.rank()

The elliptic curves in class 377520ha have rank $$1$$.

## Modular form 377520.2.a.ha

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.