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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 357390.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 357390.p1 | 357390p3 | \([1, -1, 0, -17616286545, 899957047872221]\) | \(17628594000102642361428441/248187500000000\) | \(8511949501611187500000000\) | \([2]\) | \(424673280\) | \(4.3377\) | |
| 357390.p2 | 357390p4 | \([1, -1, 0, -1621849425, -556156547875]\) | \(13756443594716753103321/7957003087464992000\) | \(272896936649373231262207008000\) | \([2]\) | \(424673280\) | \(4.3377\) | |
| 357390.p3 | 357390p2 | \([1, -1, 0, -1102009425, 14035440348125]\) | \(4315493878427398863321/16147293184000000\) | \(553794788899193250816000000\) | \([2, 2]\) | \(212336640\) | \(3.9911\) | |
| 357390.p4 | 357390p1 | \([1, -1, 0, -37377105, 420709313501]\) | \(-168380411424176601/2131914391552000\) | \(-73117089469247099240448000\) | \([2]\) | \(106168320\) | \(3.6446\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 357390.p have rank \(0\).
Complex multiplication
The elliptic curves in class 357390.p do not have complex multiplication.Modular form 357390.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
