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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 63525m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63525.bh2 | 63525m1 | \([0, -1, 1, -4033, 5715093]\) | \(-262144/509355\) | \(-14099272705546875\) | \([]\) | \(414720\) | \(1.7777\) | \(\Gamma_0(N)\)-optimal |
63525.bh1 | 63525m2 | \([0, -1, 1, -2545033, 1563665718]\) | \(-65860951343104/3493875\) | \(-96712698263671875\) | \([]\) | \(1244160\) | \(2.3270\) |
Rank
sage: E.rank()
The elliptic curves in class 63525m have rank \(1\).
Complex multiplication
The elliptic curves in class 63525m do not have complex multiplication.Modular form 63525.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.