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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 37026.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37026.bh1 | 37026y3 | \([1, -1, 1, -18071484575, -935054150461945]\) | \(505384091400037554067434625/815656731648\) | \(1053394542622620582912\) | \([2]\) | \(33177600\) | \(4.1892\) | |
| 37026.bh2 | 37026y4 | \([1, -1, 1, -18071310335, -935073083171257]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-26220957939801224820885452832\) | \([2]\) | \(66355200\) | \(4.5358\) | |
| 37026.bh3 | 37026y1 | \([1, -1, 1, -223732895, -1275017552377]\) | \(959024269496848362625/11151660319506432\) | \(14402012103810862817476608\) | \([2]\) | \(11059200\) | \(3.6399\) | \(\Gamma_0(N)\)-optimal |
| 37026.bh4 | 37026y2 | \([1, -1, 1, -45311135, -3252715708921]\) | \(-7966267523043306625/3534510366354604032\) | \(-4564706924245426403006251008\) | \([2]\) | \(22118400\) | \(3.9865\) |
Rank
sage: E.rank()
The elliptic curves in class 37026.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 37026.bh do not have complex multiplication.Modular form 37026.2.a.bh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
