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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 15210w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.q2 | 15210w1 | \([1, -1, 0, -64674, -6725120]\) | \(-3869893/300\) | \(-2319204012875100\) | \([2]\) | \(99840\) | \(1.6959\) | \(\Gamma_0(N)\)-optimal |
| 15210.q1 | 15210w2 | \([1, -1, 0, -1053324, -415828490]\) | \(16718302693/90\) | \(695761203862530\) | \([2]\) | \(199680\) | \(2.0425\) |
Rank
sage: E.rank()
The elliptic curves in class 15210w have rank \(0\).
Complex multiplication
The elliptic curves in class 15210w do not have complex multiplication.Modular form 15210.2.a.w
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.
