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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 3120.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3120.y1 | 3120x2 | \([0, 1, 0, -13640, 608628]\) | \(68523370149961/243360\) | \(996802560\) | \([2]\) | \(3840\) | \(0.94498\) | |
3120.y2 | 3120x1 | \([0, 1, 0, -840, 9588]\) | \(-16022066761/998400\) | \(-4089446400\) | \([2]\) | \(1920\) | \(0.59841\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3120.y have rank \(0\).
Complex multiplication
The elliptic curves in class 3120.y do not have complex multiplication.Modular form 3120.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.