Show commands:
SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 149058.eq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
149058.eq1 | 149058ct1 | \([1, -1, 1, -15749, -756843]\) | \(-67645179/8\) | \(-51086946456\) | \([]\) | \(331776\) | \(1.0803\) | \(\Gamma_0(N)\)-optimal |
149058.eq2 | 149058ct2 | \([1, -1, 1, 1996, -2349161]\) | \(189/512\) | \(-2383512573851136\) | \([]\) | \(995328\) | \(1.6296\) |
Rank
sage: E.rank()
The elliptic curves in class 149058.eq have rank \(1\).
Complex multiplication
The elliptic curves in class 149058.eq do not have complex multiplication.Modular form 149058.2.a.eq
sage: E.q_eigenform(10)
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.