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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 59150.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59150.m1 | 59150i1 | \([1, 1, 0, -248732500, 1509791954000]\) | \(-644487634439863642624729/896000\) | \(-2366000000000\) | \([]\) | \(4976640\) | \(3.0236\) | \(\Gamma_0(N)\)-optimal |
59150.m2 | 59150i2 | \([1, 1, 0, -248665875, 1510641278125]\) | \(-643969879566315506524489/719323136000000000\) | \(-1899462656000000000000000\) | \([]\) | \(14929920\) | \(3.5729\) |
Rank
sage: E.rank()
The elliptic curves in class 59150.m have rank \(0\).
Complex multiplication
The elliptic curves in class 59150.m do not have complex multiplication.Modular form 59150.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.