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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 30400o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30400.bo2 | 30400o1 | \([0, -1, 0, 467, 1437]\) | \(702464/475\) | \(-7600000000\) | \([2]\) | \(24576\) | \(0.58464\) | \(\Gamma_0(N)\)-optimal |
| 30400.bo1 | 30400o2 | \([0, -1, 0, -2033, 13937]\) | \(3631696/1805\) | \(462080000000\) | \([2]\) | \(49152\) | \(0.93121\) |
Rank
sage: E.rank()
The elliptic curves in class 30400o have rank \(0\).
Complex multiplication
The elliptic curves in class 30400o do not have complex multiplication.Modular form 30400.2.a.o
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.
