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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 45662c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45662.b3 | 45662c1 | \([1, 1, 0, -13444, 594404]\) | \(11134383337/316\) | \(7627471804\) | \([]\) | \(69120\) | \(0.99785\) | \(\Gamma_0(N)\)-optimal |
| 45662.b2 | 45662c2 | \([1, 1, 0, -23559, -427211]\) | \(59914169497/31554496\) | \(761648824460224\) | \([]\) | \(207360\) | \(1.5472\) | |
| 45662.b1 | 45662c3 | \([1, 1, 0, -1507574, -713096876]\) | \(15698803397448457/20709376\) | \(499873992146944\) | \([]\) | \(622080\) | \(2.0965\) |
Rank
sage: E.rank()
The elliptic curves in class 45662c have rank \(1\).
Complex multiplication
The elliptic curves in class 45662c do not have complex multiplication.Modular form 45662.2.a.c
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
