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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 83259m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83259.b3 | 83259m1 | \([0, 0, 1, -2523, -115848]\) | \(-4096/11\) | \(-4769888211099\) | \([]\) | \(151200\) | \(1.1202\) | \(\Gamma_0(N)\)-optimal |
83259.b2 | 83259m2 | \([0, 0, 1, -78213, 15249222]\) | \(-122023936/161051\) | \(-69835933298700459\) | \([]\) | \(756000\) | \(1.9249\) | |
83259.b1 | 83259m3 | \([0, 0, 1, -59192103, 175284602712]\) | \(-52893159101157376/11\) | \(-4769888211099\) | \([]\) | \(3780000\) | \(2.7297\) |
Rank
sage: E.rank()
The elliptic curves in class 83259m have rank \(1\).
Complex multiplication
The elliptic curves in class 83259m do not have complex multiplication.Modular form 83259.2.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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.