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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 14784cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14784.h4 | 14784cb1 | \([0, -1, 0, -41249, 1080513]\) | \(29609739866953/15259926528\) | \(4000298179756032\) | \([2]\) | \(92160\) | \(1.6859\) | \(\Gamma_0(N)\)-optimal |
| 14784.h2 | 14784cb2 | \([0, -1, 0, -368929, -85361471]\) | \(21184262604460873/216872764416\) | \(56851893955067904\) | \([2, 2]\) | \(184320\) | \(2.0325\) | |
| 14784.h1 | 14784cb3 | \([0, -1, 0, -5888289, -5497645887]\) | \(86129359107301290313/9166294368\) | \(2402889070804992\) | \([2]\) | \(368640\) | \(2.3790\) | |
| 14784.h3 | 14784cb4 | \([0, -1, 0, -92449, -210606911]\) | \(-333345918055753/72923718045024\) | \(-19116515143194771456\) | \([4]\) | \(368640\) | \(2.3790\) |
Rank
sage: E.rank()
The elliptic curves in class 14784cb have rank \(0\).
Complex multiplication
The elliptic curves in class 14784cb do not have complex multiplication.Modular form 14784.2.a.cb
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.
