Properties

Label 305760da
Number of curves $4$
Conductor $305760$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("da1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 305760da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
305760.da3 305760da1 \([0, -1, 0, -3250, 67600]\) \(504358336/38025\) \(286310606400\) \([2, 2]\) \(294912\) \(0.94358\) \(\Gamma_0(N)\)-optimal
305760.da1 305760da2 \([0, -1, 0, -51025, 4453345]\) \(30488290624/195\) \(93968609280\) \([2]\) \(589824\) \(1.2902\)  
305760.da4 305760da3 \([0, -1, 0, 3120, 294372]\) \(55742968/658125\) \(-39643007040000\) \([2]\) \(589824\) \(1.2902\)  
305760.da2 305760da4 \([0, -1, 0, -10600, -338120]\) \(2186875592/428415\) \(25806129323520\) \([2]\) \(589824\) \(1.2902\)  

Rank

sage: E.rank()
 

The elliptic curves in class 305760da have rank \(1\).

Complex multiplication

The elliptic curves in class 305760da do not have complex multiplication.

Modular form 305760.2.a.da

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + q^{13} - q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})\)  Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.