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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 284400.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 284400.cr1 | 284400cr3 | \([0, 0, 0, -18779475, -31323680750]\) | \(15698803397448457/20709376\) | \(966216646656000000\) | \([]\) | \(9331200\) | \(2.7270\) | |
| 284400.cr2 | 284400cr2 | \([0, 0, 0, -293475, -18350750]\) | \(59914169497/31554496\) | \(1472206565376000000\) | \([]\) | \(3110400\) | \(2.1777\) | |
| 284400.cr3 | 284400cr1 | \([0, 0, 0, -167475, 26379250]\) | \(11134383337/316\) | \(14743296000000\) | \([]\) | \(1036800\) | \(1.6284\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 284400.cr have rank \(1\).
Complex multiplication
The elliptic curves in class 284400.cr do not have complex multiplication.Modular form 284400.2.a.cr
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
