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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 25200eo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25200.fl2 | 25200eo1 | \([0, 0, 0, 15, -65]\) | \(1280/7\) | \(-2041200\) | \([]\) | \(3456\) | \(-0.10718\) | \(\Gamma_0(N)\)-optimal |
| 25200.fl1 | 25200eo2 | \([0, 0, 0, -885, -10145]\) | \(-262885120/343\) | \(-100018800\) | \([]\) | \(10368\) | \(0.44213\) |
Rank
sage: E.rank()
The elliptic curves in class 25200eo have rank \(0\).
Complex multiplication
The elliptic curves in class 25200eo do not have complex multiplication.Modular form 25200.2.a.eo
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
