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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 24150.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.bn1 | 24150bp3 | \([1, 1, 1, -72188, -2485219]\) | \(2662558086295801/1374177967680\) | \(21471530745000000\) | \([2]\) | \(207360\) | \(1.8259\) | |
24150.bn2 | 24150bp1 | \([1, 1, 1, -40313, 3098531]\) | \(463702796512201/15214500\) | \(237726562500\) | \([2]\) | \(69120\) | \(1.2766\) | \(\Gamma_0(N)\)-optimal |
24150.bn3 | 24150bp2 | \([1, 1, 1, -38563, 3382031]\) | \(-405897921250921/84358968750\) | \(-1318108886718750\) | \([2]\) | \(138240\) | \(1.6231\) | |
24150.bn4 | 24150bp4 | \([1, 1, 1, 270812, -18949219]\) | \(140574743422291079/91397357868600\) | \(-1428083716696875000\) | \([2]\) | \(414720\) | \(2.1724\) |
Rank
sage: E.rank()
The elliptic curves in class 24150.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 24150.bn do not have complex multiplication.Modular form 24150.2.a.bn
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.