Properties

Label 1815.c
Number of curves $2$
Conductor $1815$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1815.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1815.c1 1815d2 \([0, 1, 1, -5991, 176501]\) \(-196566176333824/421875\) \(-51046875\) \([]\) \(1296\) \(0.72653\)  
1815.c2 1815d1 \([0, 1, 1, -51, 380]\) \(-123633664/492075\) \(-59541075\) \([]\) \(432\) \(0.17722\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1815.c have rank \(1\).

Complex multiplication

The elliptic curves in class 1815.c do not have complex multiplication.

Modular form 1815.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{4} - q^{5} + q^{7} + q^{9} - 2q^{12} - 2q^{13} - q^{15} + 4q^{16} - 6q^{17} + 7q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.