Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 35520.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35520.k1 | 35520bq4 | \([0, -1, 0, -21824321, -39235457055]\) | \(4385367890843575421521/24975000000\) | \(6547046400000000\) | \([2]\) | \(1327104\) | \(2.6465\) | |
| 35520.k2 | 35520bq6 | \([0, -1, 0, -19400001, 32752486881]\) | \(3080272010107543650001/15465841417699560\) | \(4054277532601433456640\) | \([2]\) | \(2654208\) | \(2.9931\) | |
| 35520.k3 | 35520bq3 | \([0, -1, 0, -1876801, -110522399]\) | \(2788936974993502801/1593609593601600\) | \(417755193305097830400\) | \([2, 2]\) | \(1327104\) | \(2.6465\) | |
| 35520.k4 | 35520bq2 | \([0, -1, 0, -1364801, -611975199]\) | \(1072487167529950801/2554882560000\) | \(669747133808640000\) | \([2, 2]\) | \(663552\) | \(2.3000\) | |
| 35520.k5 | 35520bq1 | \([0, -1, 0, -54081, -16646175]\) | \(-66730743078481/419010969600\) | \(-109841211614822400\) | \([2]\) | \(331776\) | \(1.9534\) | \(\Gamma_0(N)\)-optimal |
| 35520.k6 | 35520bq5 | \([0, -1, 0, 7454399, -888744479]\) | \(174751791402194852399/102423900876336360\) | \(-26849811071326318755840\) | \([2]\) | \(2654208\) | \(2.9931\) |
Rank
sage: E.rank()
The elliptic curves in class 35520.k have rank \(0\).
Complex multiplication
The elliptic curves in class 35520.k do not have complex multiplication.Modular form 35520.2.a.k
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
