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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 284592br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 284592.br4 | 284592br1 | \([0, -1, 0, -61141824, 60896959488]\) | \(29609739866953/15259926528\) | \(13027369807663227293663232\) | \([2]\) | \(66355200\) | \(3.5112\) | \(\Gamma_0(N)\)-optimal |
| 284592.br2 | 284592br2 | \([0, -1, 0, -546845504, -4878126621696]\) | \(21184262604460873/216872764416\) | \(185143860166916940238946304\) | \([2, 2]\) | \(132710400\) | \(3.8578\) | |
| 284592.br3 | 284592br3 | \([0, -1, 0, -137033024, -12020338523136]\) | \(-333345918055753/72923718045024\) | \(-62254837268001014346248749056\) | \([2]\) | \(265420800\) | \(4.2044\) | |
| 284592.br1 | 284592br4 | \([0, -1, 0, -8727916864, -313841195174912]\) | \(86129359107301290313/9166294368\) | \(7825247800422219934728192\) | \([2]\) | \(265420800\) | \(4.2044\) |
Rank
sage: E.rank()
The elliptic curves in class 284592br have rank \(0\).
Complex multiplication
The elliptic curves in class 284592br do not have complex multiplication.Modular form 284592.2.a.br
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
