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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 28899.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28899.k1 | 28899c3 | \([0, 0, 1, -1170156, 487207269]\) | \(-50357871050752/19\) | \(-66856131459\) | \([]\) | \(155520\) | \(1.8652\) | |
| 28899.k2 | 28899c2 | \([0, 0, 1, -14196, 692604]\) | \(-89915392/6859\) | \(-24135063456699\) | \([]\) | \(51840\) | \(1.3159\) | |
| 28899.k3 | 28899c1 | \([0, 0, 1, 1014, 549]\) | \(32768/19\) | \(-66856131459\) | \([]\) | \(17280\) | \(0.76661\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28899.k have rank \(0\).
Complex multiplication
The elliptic curves in class 28899.k do not have complex multiplication.Modular form 28899.2.a.k
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
