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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 74025.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74025.y1 | 74025l2 | \([0, 0, 1, -175500, -28303594]\) | \(-77750599680/16121\) | \(-123949079296875\) | \([]\) | \(354240\) | \(1.7009\) | |
74025.y2 | 74025l1 | \([0, 0, 1, 750, -132969]\) | \(4423680/726761\) | \(-7665057421875\) | \([3]\) | \(118080\) | \(1.1516\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74025.y have rank \(0\).
Complex multiplication
The elliptic curves in class 74025.y do not have complex multiplication.Modular form 74025.2.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 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.