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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 179088bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179088.t3 | 179088bj1 | \([0, -1, 0, -10288, -1097792]\) | \(-29403487464625/110884842432\) | \(-454184314601472\) | \([2]\) | \(497664\) | \(1.4981\) | \(\Gamma_0(N)\)-optimal |
| 179088.t2 | 179088bj2 | \([0, -1, 0, -234928, -43689536]\) | \(350082141630936625/555332456952\) | \(2274641743675392\) | \([2]\) | \(995328\) | \(1.8447\) | |
| 179088.t4 | 179088bj3 | \([0, -1, 0, 90512, 26142400]\) | \(20020616659055375/83832462778428\) | \(-343377767540441088\) | \([2]\) | \(1492992\) | \(2.0474\) | |
| 179088.t1 | 179088bj4 | \([0, -1, 0, -964048, 322262848]\) | \(24191354664255948625/3068177831138238\) | \(12567256396342222848\) | \([2]\) | \(2985984\) | \(2.3940\) |
Rank
sage: E.rank()
The elliptic curves in class 179088bj have rank \(1\).
Complex multiplication
The elliptic curves in class 179088bj do not have complex multiplication.Modular form 179088.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
