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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 16905.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16905.w1 | 16905p3 | \([1, 1, 0, -210382, -37229429]\) | \(8753151307882969/65205\) | \(7671303045\) | \([2]\) | \(67584\) | \(1.4913\) | |
| 16905.w2 | 16905p2 | \([1, 1, 0, -13157, -585024]\) | \(2141202151369/5832225\) | \(686155439025\) | \([2, 2]\) | \(33792\) | \(1.1447\) | |
| 16905.w3 | 16905p4 | \([1, 1, 0, -8012, -1040871]\) | \(-483551781049/3672913125\) | \(-432114556243125\) | \([4]\) | \(67584\) | \(1.4913\) | |
| 16905.w4 | 16905p1 | \([1, 1, 0, -1152, -1581]\) | \(1439069689/828345\) | \(97453960905\) | \([2]\) | \(16896\) | \(0.79814\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16905.w have rank \(0\).
Complex multiplication
The elliptic curves in class 16905.w do not have complex multiplication.Modular form 16905.2.a.w
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 LMFDB 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 LMFDB labels.
