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SageMath
E = EllipticCurve("em1")
E.isogeny_class()
Elliptic curves in class 46800.em
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.em1 | 46800ch2 | \([0, 0, 0, -1437075, -663072750]\) | \(260549802603/4225\) | \(5322283200000000\) | \([2]\) | \(589824\) | \(2.1500\) | |
| 46800.em2 | 46800ch1 | \([0, 0, 0, -87075, -11022750]\) | \(-57960603/8125\) | \(-10235160000000000\) | \([2]\) | \(294912\) | \(1.8034\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.em have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.em do not have complex multiplication.Modular form 46800.2.a.em
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 LMFDB 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 LMFDB labels.
