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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 85800.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85800.y1 | 85800bv4 | \([0, -1, 0, -381408, 90790812]\) | \(383507853966436/57915\) | \(926640000000\) | \([2]\) | \(491520\) | \(1.7025\) | |
| 85800.y2 | 85800bv2 | \([0, -1, 0, -23908, 1415812]\) | \(377843214544/4601025\) | \(18404100000000\) | \([2, 2]\) | \(245760\) | \(1.3559\) | |
| 85800.y3 | 85800bv3 | \([0, -1, 0, -4408, 3638812]\) | \(-592143556/356874375\) | \(-5709990000000000\) | \([2]\) | \(491520\) | \(1.7025\) | |
| 85800.y4 | 85800bv1 | \([0, -1, 0, -2783, -20688]\) | \(9538484224/4712565\) | \(1178141250000\) | \([2]\) | \(122880\) | \(1.0093\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85800.y have rank \(1\).
Complex multiplication
The elliptic curves in class 85800.y do not have complex multiplication.Modular form 85800.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
