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SageMath
E = EllipticCurve("hk1")
E.isogeny_class()
Elliptic curves in class 202800.hk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.hk1 | 202800m2 | \([0, 1, 0, -4429208, -3230354412]\) | \(248858189/27378\) | \(1057187014416000000000\) | \([2]\) | \(10321920\) | \(2.7676\) | |
| 202800.hk2 | 202800m1 | \([0, 1, 0, -1049208, 359205588]\) | \(3307949/468\) | \(18071572896000000000\) | \([2]\) | \(5160960\) | \(2.4210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202800.hk have rank \(0\).
Complex multiplication
The elliptic curves in class 202800.hk do not have complex multiplication.Modular form 202800.2.a.hk
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.
