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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 46800s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.bn2 | 46800s1 | \([0, 0, 0, -75, 162250]\) | \(-4/975\) | \(-11372400000000\) | \([2]\) | \(73728\) | \(1.1841\) | \(\Gamma_0(N)\)-optimal |
| 46800.bn1 | 46800s2 | \([0, 0, 0, -45075, 3627250]\) | \(434163602/7605\) | \(177409440000000\) | \([2]\) | \(147456\) | \(1.5306\) |
Rank
sage: E.rank()
The elliptic curves in class 46800s have rank \(2\).
Complex multiplication
The elliptic curves in class 46800s do not have complex multiplication.Modular form 46800.2.a.s
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.
