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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 37440.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.m1 | 37440em2 | \([0, 0, 0, -26508, -1488112]\) | \(10779215329/1232010\) | \(235440777461760\) | \([2]\) | \(147456\) | \(1.4900\) | |
37440.m2 | 37440em1 | \([0, 0, 0, 2292, -117232]\) | \(6967871/35100\) | \(-6707714457600\) | \([2]\) | \(73728\) | \(1.1434\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37440.m have rank \(2\).
Complex multiplication
The elliptic curves in class 37440.m do not have complex multiplication.Modular form 37440.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.