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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 298816bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 298816.bc4 | 298816bc1 | \([0, 0, 0, -2881196, -1899702576]\) | \(-10090256344188054273/107965577101312\) | \(-28302528243646332928\) | \([2]\) | \(7372800\) | \(2.5488\) | \(\Gamma_0(N)\)-optimal |
| 298816.bc3 | 298816bc2 | \([0, 0, 0, -46216876, -120934148400]\) | \(41647175116728660507393/4693358285056\) | \(1230335714277720064\) | \([2, 2]\) | \(14745600\) | \(2.8954\) | |
| 298816.bc2 | 298816bc3 | \([0, 0, 0, -46334636, -120286892336]\) | \(41966336340198080824833/442001722607124848\) | \(115868099571122136154112\) | \([2]\) | \(29491200\) | \(3.2419\) | |
| 298816.bc1 | 298816bc4 | \([0, 0, 0, -739469996, -7739785937200]\) | \(170586815436843383543017473/2166416\) | \(567912955904\) | \([2]\) | \(29491200\) | \(3.2419\) |
Rank
sage: E.rank()
The elliptic curves in class 298816bc have rank \(1\).
Complex multiplication
The elliptic curves in class 298816bc do not have complex multiplication.Modular form 298816.2.a.bc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
