Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 149058ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 149058.gb2 | 149058ba1 | \([1, -1, 1, -1553, 54695]\) | \(-2401/6\) | \(-1034510665734\) | \([]\) | \(225792\) | \(0.99330\) | \(\Gamma_0(N)\)-optimal |
| 149058.gb1 | 149058ba2 | \([1, -1, 1, -214493, -39616027]\) | \(-6329617441/279936\) | \(-48266129620485504\) | \([]\) | \(1580544\) | \(1.9663\) |
Rank
sage: E.rank()
The elliptic curves in class 149058ba have rank \(0\).
Complex multiplication
The elliptic curves in class 149058ba do not have complex multiplication.Modular form 149058.2.a.ba
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.
