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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 81120.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81120.v1 | 81120bg4 | \([0, -1, 0, -175985, 28474497]\) | \(30488290624/195\) | \(3855268884480\) | \([4]\) | \(258048\) | \(1.5997\) | |
81120.v2 | 81120bg3 | \([0, -1, 0, -36560, -2176188]\) | \(2186875592/428415\) | \(1058753217400320\) | \([2]\) | \(258048\) | \(1.5997\) | |
81120.v3 | 81120bg1 | \([0, -1, 0, -11210, 429792]\) | \(504358336/38025\) | \(11746522382400\) | \([2, 2]\) | \(129024\) | \(1.2531\) | \(\Gamma_0(N)\)-optimal |
81120.v4 | 81120bg2 | \([0, -1, 0, 10760, 1888600]\) | \(55742968/658125\) | \(-1626441560640000\) | \([2]\) | \(258048\) | \(1.5997\) |
Rank
sage: E.rank()
The elliptic curves in class 81120.v have rank \(1\).
Complex multiplication
The elliptic curves in class 81120.v do not have complex multiplication.Modular form 81120.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.