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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 290400.ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290400.ca1 | 290400ca4 | \([0, -1, 0, -246033, -46848063]\) | \(14526784/15\) | \(1700698560000000\) | \([2]\) | \(1966080\) | \(1.8404\) | |
290400.ca2 | 290400ca2 | \([0, -1, 0, -170408, 26886312]\) | \(38614472/405\) | \(5739857640000000\) | \([2]\) | \(1966080\) | \(1.8404\) | |
290400.ca3 | 290400ca1 | \([0, -1, 0, -19158, -338688]\) | \(438976/225\) | \(398601225000000\) | \([2, 2]\) | \(983040\) | \(1.4938\) | \(\Gamma_0(N)\)-optimal |
290400.ca4 | 290400ca3 | \([0, -1, 0, 71592, -2698188]\) | \(2863288/1875\) | \(-26573415000000000\) | \([2]\) | \(1966080\) | \(1.8404\) |
Rank
sage: E.rank()
The elliptic curves in class 290400.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 290400.ca do not have complex multiplication.Modular form 290400.2.a.ca
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.