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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 6720.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6720.y1 | 6720n4 | \([0, -1, 0, -1505, 22977]\) | \(11512557512/2835\) | \(92897280\) | \([2]\) | \(4096\) | \(0.51684\) | |
6720.y2 | 6720n3 | \([0, -1, 0, -705, -6783]\) | \(1184287112/36015\) | \(1180139520\) | \([2]\) | \(4096\) | \(0.51684\) | |
6720.y3 | 6720n2 | \([0, -1, 0, -105, 297]\) | \(31554496/11025\) | \(45158400\) | \([2, 2]\) | \(2048\) | \(0.17027\) | |
6720.y4 | 6720n1 | \([0, -1, 0, 20, 22]\) | \(13144256/13125\) | \(-840000\) | \([2]\) | \(1024\) | \(-0.17631\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6720.y have rank \(1\).
Complex multiplication
The elliptic curves in class 6720.y do not have complex multiplication.Modular form 6720.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.