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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 37200.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37200.m1 | 37200bx2 | \([0, -1, 0, -264408, 52419312]\) | \(31942518433489/27900\) | \(1785600000000\) | \([2]\) | \(184320\) | \(1.6513\) | |
| 37200.m2 | 37200bx1 | \([0, -1, 0, -16408, 835312]\) | \(-7633736209/230640\) | \(-14760960000000\) | \([2]\) | \(92160\) | \(1.3047\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37200.m have rank \(1\).
Complex multiplication
The elliptic curves in class 37200.m do not have complex multiplication.Modular form 37200.2.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.
