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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 177744.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177744.bb1 | 177744bv4 | \([0, -1, 0, -12835575768, -557002065050640]\) | \(385693937170561837203625/2159357734550274048\) | \(1309337362035408215610608320512\) | \([2]\) | \(364953600\) | \(4.6213\) | |
| 177744.bb2 | 177744bv2 | \([0, -1, 0, -947930088, 10703213724528]\) | \(155355156733986861625/8291568305839392\) | \(5027633911231112339208142848\) | \([2]\) | \(121651200\) | \(4.0720\) | |
| 177744.bb3 | 177744bv3 | \([0, -1, 0, -354899928, -18356064877584]\) | \(-8152944444844179625/235342826399858688\) | \(-142701299817987073443650076672\) | \([2]\) | \(182476800\) | \(4.2747\) | |
| 177744.bb4 | 177744bv1 | \([0, -1, 0, 39310872, 668106814320]\) | \(11079872671250375/324440155855872\) | \(-196725911140034836030291968\) | \([2]\) | \(60825600\) | \(3.7254\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 177744.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 177744.bb do not have complex multiplication.Modular form 177744.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
