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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 8976w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8976.p4 | 8976w1 | \([0, -1, 0, -93552, 8644032]\) | \(22106889268753393/4969545596928\) | \(20355258765017088\) | \([2]\) | \(64512\) | \(1.8423\) | \(\Gamma_0(N)\)-optimal |
| 8976.p2 | 8976w2 | \([0, -1, 0, -1404272, 640935360]\) | \(74768347616680342513/5615307472896\) | \(23000299408982016\) | \([2, 2]\) | \(129024\) | \(2.1888\) | |
| 8976.p1 | 8976w3 | \([0, -1, 0, -22467952, 40998946240]\) | \(306234591284035366263793/1727485056\) | \(7075778789376\) | \([2]\) | \(258048\) | \(2.5354\) | |
| 8976.p3 | 8976w4 | \([0, -1, 0, -1312112, 728597952]\) | \(-60992553706117024753/20624795251201152\) | \(-84479161348919918592\) | \([4]\) | \(258048\) | \(2.5354\) |
Rank
sage: E.rank()
The elliptic curves in class 8976w have rank \(0\).
Complex multiplication
The elliptic curves in class 8976w do not have complex multiplication.Modular form 8976.2.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 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.
