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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 452400m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
452400.m3 | 452400m1 | \([0, -1, 0, -709008, -229543488]\) | \(615882348586441/21715200\) | \(1389772800000000\) | \([2]\) | \(7077888\) | \(1.9955\) | \(\Gamma_0(N)\)-optimal* |
452400.m2 | 452400m2 | \([0, -1, 0, -741008, -207655488]\) | \(703093388853961/115124490000\) | \(7367967360000000000\) | \([2, 2]\) | \(14155776\) | \(2.3420\) | \(\Gamma_0(N)\)-optimal* |
452400.m1 | 452400m3 | \([0, -1, 0, -3341008, 2153144512]\) | \(64443098670429961/6032611833300\) | \(386087157331200000000\) | \([2]\) | \(28311552\) | \(2.6886\) | \(\Gamma_0(N)\)-optimal* |
452400.m4 | 452400m4 | \([0, -1, 0, 1346992, -1168135488]\) | \(4223169036960119/11647532812500\) | \(-745442100000000000000\) | \([2]\) | \(28311552\) | \(2.6886\) |
Rank
sage: E.rank()
The elliptic curves in class 452400m have rank \(1\).
Complex multiplication
The elliptic curves in class 452400m do not have complex multiplication.Modular form 452400.2.a.m
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 Cremona 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 Cremona labels.