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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 185020.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185020.o1 | 185020m4 | \([0, -1, 0, -5971380, -5614436728]\) | \(154639330142416/33275\) | \(5066942977606400\) | \([2]\) | \(5225472\) | \(2.3981\) | |
| 185020.o2 | 185020m3 | \([0, -1, 0, -374525, -86982730]\) | \(610462990336/8857805\) | \(84301263789926480\) | \([2]\) | \(2612736\) | \(2.0515\) | |
| 185020.o3 | 185020m2 | \([0, -1, 0, -84380, -5303128]\) | \(436334416/171875\) | \(26172226124000000\) | \([2]\) | \(1741824\) | \(1.8488\) | |
| 185020.o4 | 185020m1 | \([0, -1, 0, -38125, 2819250]\) | \(643956736/15125\) | \(143947243682000\) | \([2]\) | \(870912\) | \(1.5022\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185020.o have rank \(2\).
Complex multiplication
The elliptic curves in class 185020.o do not have complex multiplication.Modular form 185020.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
