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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 44352bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.ea4 | 44352bl1 | \([0, 0, 0, -371244, 28802608]\) | \(29609739866953/15259926528\) | \(2916217373042147328\) | \([2]\) | \(737280\) | \(2.2352\) | \(\Gamma_0(N)\)-optimal |
| 44352.ea2 | 44352bl2 | \([0, 0, 0, -3320364, -2308080080]\) | \(21184262604460873/216872764416\) | \(41445030693244502016\) | \([2, 2]\) | \(1474560\) | \(2.5818\) | |
| 44352.ea3 | 44352bl3 | \([0, 0, 0, -832044, -5687218640]\) | \(-333345918055753/72923718045024\) | \(-13935939539388988391424\) | \([2]\) | \(2949120\) | \(2.9283\) | |
| 44352.ea1 | 44352bl4 | \([0, 0, 0, -52994604, -148489433552]\) | \(86129359107301290313/9166294368\) | \(1751706132616839168\) | \([2]\) | \(2949120\) | \(2.9283\) |
Rank
sage: E.rank()
The elliptic curves in class 44352bl have rank \(1\).
Complex multiplication
The elliptic curves in class 44352bl do not have complex multiplication.Modular form 44352.2.a.bl
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.
