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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 15246y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15246.y2 | 15246y1 | \([1, -1, 0, -31785, 2225933]\) | \(-2749884201/54208\) | \(-70007895663552\) | \([2]\) | \(92160\) | \(1.4497\) | \(\Gamma_0(N)\)-optimal |
15246.y1 | 15246y2 | \([1, -1, 0, -510945, 140703173]\) | \(11422548526761/4312\) | \(5568809882328\) | \([2]\) | \(184320\) | \(1.7963\) |
Rank
sage: E.rank()
The elliptic curves in class 15246y have rank \(0\).
Complex multiplication
The elliptic curves in class 15246y do not have complex multiplication.Modular form 15246.2.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.