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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 149058.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
149058.q1 | 149058es2 | \([1, -1, 0, -53028936, -149379438272]\) | \(-16591834777/98304\) | \(-97710049203552730054656\) | \([]\) | \(21772800\) | \(3.2517\) | |
149058.q2 | 149058es1 | \([1, -1, 0, 1749879, -1093186067]\) | \(596183/864\) | \(-858779729328100166496\) | \([]\) | \(7257600\) | \(2.7023\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 149058.q have rank \(1\).
Complex multiplication
The elliptic curves in class 149058.q do not have complex multiplication.Modular form 149058.2.a.q
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.