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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 137904y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
137904.a2 | 137904y1 | \([0, -1, 0, -15760, -1093184]\) | \(-48109395853/30081024\) | \(-270696487845888\) | \([2]\) | \(663552\) | \(1.4710\) | \(\Gamma_0(N)\)-optimal |
137904.a1 | 137904y2 | \([0, -1, 0, -282000, -57536064]\) | \(275602131611533/53934336\) | \(485350343442432\) | \([2]\) | \(1327104\) | \(1.8176\) |
Rank
sage: E.rank()
The elliptic curves in class 137904y have rank \(0\).
Complex multiplication
The elliptic curves in class 137904y do not have complex multiplication.Modular form 137904.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.