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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 149058bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 149058.hh2 | 149058bx1 | \([1, -1, 1, -76082, -18608313]\) | \(-2401/6\) | \(-121709145312939366\) | \([]\) | \(1580544\) | \(1.9663\) | \(\Gamma_0(N)\)-optimal |
| 149058.hh1 | 149058bx2 | \([1, -1, 1, -10510142, 13609317453]\) | \(-6329617441/279936\) | \(-5678461883720499060096\) | \([]\) | \(11063808\) | \(2.9392\) |
Rank
sage: E.rank()
The elliptic curves in class 149058bx have rank \(1\).
Complex multiplication
The elliptic curves in class 149058bx do not have complex multiplication.Modular form 149058.2.a.bx
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
