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Properties

Label 1425.c
Number of curves $4$
Conductor $1425$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 1425.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1425.c1 1425h3 \([1, 0, 0, -150188, -22415133]\) \(23977812996389881/146611125\) \(2290798828125\) \([2]\) \(6912\) \(1.5589\)  
1425.c2 1425h4 \([1, 0, 0, -30938, 1693617]\) \(209595169258201/41748046875\) \(652313232421875\) \([2]\) \(6912\) \(1.5589\)  
1425.c3 1425h2 \([1, 0, 0, -9563, -337008]\) \(6189976379881/456890625\) \(7138916015625\) \([2, 2]\) \(3456\) \(1.2123\)  
1425.c4 1425h1 \([1, 0, 0, 562, -23133]\) \(1256216039/15582375\) \(-243474609375\) \([4]\) \(1728\) \(0.86571\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1425.c have rank \(0\).

Complex multiplication

The elliptic curves in class 1425.c do not have complex multiplication.

Modular form 1425.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} - 4 q^{7} + 3 q^{8} + q^{9} + 4 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} - q^{16} - 2 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.