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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 388416.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388416.y1 | 388416y2 | \([0, -1, 0, -39009, -2952351]\) | \(20389313444/1323\) | \(425977380864\) | \([2]\) | \(884736\) | \(1.2885\) | |
388416.y2 | 388416y1 | \([0, -1, 0, -2289, -51471]\) | \(-16484816/5103\) | \(-410763902976\) | \([2]\) | \(442368\) | \(0.94196\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388416.y have rank \(1\).
Complex multiplication
The elliptic curves in class 388416.y do not have complex multiplication.Modular form 388416.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.