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SageMath
E = EllipticCurve("mn1")
E.isogeny_class()
Elliptic curves in class 369600.mn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.mn1 | 369600mn4 | \([0, 1, 0, -1409633, -644647137]\) | \(75627935783569/396165\) | \(1622691840000000\) | \([2]\) | \(4718592\) | \(2.1146\) | |
369600.mn2 | 369600mn2 | \([0, 1, 0, -89633, -9727137]\) | \(19443408769/1334025\) | \(5464166400000000\) | \([2, 2]\) | \(2359296\) | \(1.7680\) | |
369600.mn3 | 369600mn1 | \([0, 1, 0, -17633, 712863]\) | \(148035889/31185\) | \(127733760000000\) | \([2]\) | \(1179648\) | \(1.4214\) | \(\Gamma_0(N)\)-optimal |
369600.mn4 | 369600mn3 | \([0, 1, 0, 78367, -41815137]\) | \(12994449551/192163125\) | \(-787100160000000000\) | \([2]\) | \(4718592\) | \(2.1146\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.mn have rank \(1\).
Complex multiplication
The elliptic curves in class 369600.mn do not have complex multiplication.Modular form 369600.2.a.mn
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.