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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 7800.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7800.k1 | 7800m3 | \([0, -1, 0, -41408, -3217188]\) | \(490757540836/2142075\) | \(34273200000000\) | \([2]\) | \(36864\) | \(1.4500\) | |
7800.k2 | 7800m2 | \([0, -1, 0, -3908, 7812]\) | \(1650587344/950625\) | \(3802500000000\) | \([2, 2]\) | \(18432\) | \(1.1035\) | |
7800.k3 | 7800m1 | \([0, -1, 0, -2783, 57312]\) | \(9538484224/26325\) | \(6581250000\) | \([2]\) | \(9216\) | \(0.75689\) | \(\Gamma_0(N)\)-optimal |
7800.k4 | 7800m4 | \([0, -1, 0, 15592, 46812]\) | \(26198797244/15234375\) | \(-243750000000000\) | \([2]\) | \(36864\) | \(1.4500\) |
Rank
sage: E.rank()
The elliptic curves in class 7800.k have rank \(0\).
Complex multiplication
The elliptic curves in class 7800.k do not have complex multiplication.Modular form 7800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.