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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 24400u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24400.q3 | 24400u1 | \([0, 0, 0, -65675, -6455750]\) | \(489490178841/1952000\) | \(124928000000000\) | \([2]\) | \(55296\) | \(1.5617\) | \(\Gamma_0(N)\)-optimal |
| 24400.q2 | 24400u2 | \([0, 0, 0, -97675, 488250]\) | \(1610252558361/930250000\) | \(59536000000000000\) | \([2, 2]\) | \(110592\) | \(1.9083\) | |
| 24400.q4 | 24400u3 | \([0, 0, 0, 390325, 3904250]\) | \(102759703687719/59570312500\) | \(-3812500000000000000\) | \([2]\) | \(221184\) | \(2.2549\) | |
| 24400.q1 | 24400u4 | \([0, 0, 0, -1097675, 441488250]\) | \(2285414915318361/6922920500\) | \(443066912000000000\) | \([4]\) | \(221184\) | \(2.2549\) |
Rank
sage: E.rank()
The elliptic curves in class 24400u have rank \(1\).
Complex multiplication
The elliptic curves in class 24400u do not have complex multiplication.Modular form 24400.2.a.u
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.
