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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 41280.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41280.v1 | 41280y4 | \([0, -1, 0, -36705, 2718945]\) | \(41725476313778/17415\) | \(2282618880\) | \([2]\) | \(98304\) | \(1.1403\) | |
41280.v2 | 41280y2 | \([0, -1, 0, -2305, 42625]\) | \(20674973956/416025\) | \(27264614400\) | \([2, 2]\) | \(49152\) | \(0.79368\) | |
41280.v3 | 41280y1 | \([0, -1, 0, -305, -975]\) | \(192143824/80625\) | \(1320960000\) | \([2]\) | \(24576\) | \(0.44711\) | \(\Gamma_0(N)\)-optimal |
41280.v4 | 41280y3 | \([0, -1, 0, 95, 124705]\) | \(715822/51282015\) | \(-6721636270080\) | \([2]\) | \(98304\) | \(1.1403\) |
Rank
sage: E.rank()
The elliptic curves in class 41280.v have rank \(1\).
Complex multiplication
The elliptic curves in class 41280.v do not have complex multiplication.Modular form 41280.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.