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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 333270.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333270.bq1 | 333270bq3 | \([1, -1, 0, -175776596199, 28364484932214493]\) | \(5565604209893236690185614401/229307220930246900000\) | \(24746414064001281479794698900000\) | \([2]\) | \(2595225600\) | \(5.1052\) | |
333270.bq2 | 333270bq4 | \([1, -1, 0, -53588768679, -4403281083996515]\) | \(157706830105239346386477121/13650704956054687500000\) | \(1473159003618124703979492187500000\) | \([2]\) | \(2595225600\) | \(5.1052\) | |
333270.bq3 | 333270bq2 | \([1, -1, 0, -11522096199, 397561086114493]\) | \(1567558142704512417614401/274462175610000000000\) | \(29619453827046040654410000000000\) | \([2, 2]\) | \(1297612800\) | \(4.7587\) | |
333270.bq4 | 333270bq1 | \([1, -1, 0, 1372977081, 35588642100925]\) | \(2652277923951208297919/6605028468326400000\) | \(-712802539399496078337638400000\) | \([2]\) | \(648806400\) | \(4.4121\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333270.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 333270.bq do not have complex multiplication.Modular form 333270.2.a.bq
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.