Properties

 Label 10304bd Number of curves $2$ Conductor $10304$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

Elliptic curves in class 10304bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.be2 10304bd1 $$[0, -1, 0, -113, -559]$$ $$-9826000/3703$$ $$-60669952$$ $$$$ $$2560$$ $$0.20324$$ $$\Gamma_0(N)$$-optimal
10304.be1 10304bd2 $$[0, -1, 0, -1953, -32575]$$ $$12576878500/1127$$ $$73859072$$ $$$$ $$5120$$ $$0.54982$$

Rank

sage: E.rank()

The elliptic curves in class 10304bd have rank $$1$$.

Complex multiplication

The elliptic curves in class 10304bd do not have complex multiplication.

Modular form 10304.2.a.bd

sage: E.q_eigenform(10)

$$q + 2 q^{3} + q^{7} + q^{9} + 4 q^{11} - 6 q^{13} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels. 