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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 35574.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35574.bj1 | 35574bg4 | \([1, 0, 1, -7968700, 8657569358]\) | \(268498407453697/252\) | \(52522439782428\) | \([2]\) | \(983040\) | \(2.3610\) | |
| 35574.bj2 | 35574bg6 | \([1, 0, 1, -5419230, -4809561242]\) | \(84448510979617/933897762\) | \(194645194315830460818\) | \([2]\) | \(1966080\) | \(2.7076\) | |
| 35574.bj3 | 35574bg3 | \([1, 0, 1, -616740, 65926606]\) | \(124475734657/63011844\) | \(13133078500276774116\) | \([2, 2]\) | \(983040\) | \(2.3610\) | |
| 35574.bj4 | 35574bg2 | \([1, 0, 1, -498160, 135177326]\) | \(65597103937/63504\) | \(13235654825171856\) | \([2, 2]\) | \(491520\) | \(2.0144\) | |
| 35574.bj5 | 35574bg1 | \([1, 0, 1, -23840, 3126638]\) | \(-7189057/16128\) | \(-3361436146075392\) | \([2]\) | \(245760\) | \(1.6679\) | \(\Gamma_0(N)\)-optimal |
| 35574.bj6 | 35574bg5 | \([1, 0, 1, 2288470, 509842694]\) | \(6359387729183/4218578658\) | \(-879246204493019540562\) | \([2]\) | \(1966080\) | \(2.7076\) |
Rank
sage: E.rank()
The elliptic curves in class 35574.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 35574.bj do not have complex multiplication.Modular form 35574.2.a.bj
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.
