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SageMath
E = EllipticCurve("hc1")
E.isogeny_class()
Elliptic curves in class 262080.hc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 262080.hc1 | 262080hc1 | \([0, 0, 0, -17148, -799472]\) | \(46689225424/3901625\) | \(46600759296000\) | \([2]\) | \(884736\) | \(1.3647\) | \(\Gamma_0(N)\)-optimal |
| 262080.hc2 | 262080hc2 | \([0, 0, 0, 18132, -3664208]\) | \(13799183324/129390625\) | \(-6181733376000000\) | \([2]\) | \(1769472\) | \(1.7112\) |
Rank
sage: E.rank()
The elliptic curves in class 262080.hc have rank \(0\).
Complex multiplication
The elliptic curves in class 262080.hc do not have complex multiplication.Modular form 262080.2.a.hc
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
