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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 152880.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152880.k1 | 152880dy2 | \([0, -1, 0, -668376, -210096144]\) | \(68523370149961/243360\) | \(117272824381440\) | \([2]\) | \(1382400\) | \(1.9179\) | |
152880.k2 | 152880dy1 | \([0, -1, 0, -41176, -3371024]\) | \(-16022066761/998400\) | \(-481119279513600\) | \([2]\) | \(691200\) | \(1.5714\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152880.k have rank \(0\).
Complex multiplication
The elliptic curves in class 152880.k do not have complex multiplication.Modular form 152880.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.