Properties

Label 3150.i
Number of curves $6$
Conductor $3150$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.i1 3150l6 \([1, -1, 0, -614367, 185502541]\) \(2251439055699625/25088\) \(285768000000\) \([2]\) \(20736\) \(1.7671\)  
3150.i2 3150l5 \([1, -1, 0, -38367, 2910541]\) \(-548347731625/1835008\) \(-20901888000000\) \([2]\) \(10368\) \(1.4206\)  
3150.i3 3150l4 \([1, -1, 0, -7992, 227416]\) \(4956477625/941192\) \(10720765125000\) \([2]\) \(6912\) \(1.2178\)  
3150.i4 3150l2 \([1, -1, 0, -2367, -43709]\) \(128787625/98\) \(1116281250\) \([2]\) \(2304\) \(0.66851\)  
3150.i5 3150l1 \([1, -1, 0, -117, -959]\) \(-15625/28\) \(-318937500\) \([2]\) \(1152\) \(0.32194\) \(\Gamma_0(N)\)-optimal
3150.i6 3150l3 \([1, -1, 0, 1008, 20416]\) \(9938375/21952\) \(-250047000000\) \([2]\) \(3456\) \(0.87125\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3150.i have rank \(0\).

Complex multiplication

The elliptic curves in class 3150.i do not have complex multiplication.

Modular form 3150.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + 4q^{13} + q^{14} + q^{16} + 6q^{17} + 2q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.