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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 211420.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
211420.n1 | 211420m4 | \([0, -1, 0, -6823420, 6862702632]\) | \(154639330142416/33275\) | \(7560111356230400\) | \([2]\) | \(6220800\) | \(2.4314\) | |
211420.n2 | 211420m3 | \([0, -1, 0, -427965, 106543970]\) | \(610462990336/8857805\) | \(125781352689283280\) | \([2]\) | \(3110400\) | \(2.0849\) | |
211420.n3 | 211420m2 | \([0, -1, 0, -96420, 6544232]\) | \(436334416/171875\) | \(39050161964000000\) | \([2]\) | \(2073600\) | \(1.8821\) | |
211420.n4 | 211420m1 | \([0, -1, 0, -43565, -3413650]\) | \(643956736/15125\) | \(214775890802000\) | \([2]\) | \(1036800\) | \(1.5356\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 211420.n have rank \(1\).
Complex multiplication
The elliptic curves in class 211420.n do not have complex multiplication.Modular form 211420.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.