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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 377520.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.u1 | 377520u4 | \([0, -1, 0, -310584776, -2106622452240]\) | \(456612868287073618849/12544848030000\) | \(91029354581503303680000\) | \([2]\) | \(70778880\) | \(3.5088\) | |
| 377520.u2 | 377520u3 | \([0, -1, 0, -86628296, 280596762096]\) | \(9908022260084596129/1047363281250000\) | \(7599996690000000000000000\) | \([2]\) | \(70778880\) | \(3.5088\) | |
| 377520.u3 | 377520u2 | \([0, -1, 0, -20184776, -30146292240]\) | \(125337052492018849/18404100000000\) | \(133545925837209600000000\) | \([2, 2]\) | \(35389440\) | \(3.1623\) | |
| 377520.u4 | 377520u1 | \([0, -1, 0, 2117944, -2562288144]\) | \(144794100308831/474439680000\) | \(-3442683223820206080000\) | \([2]\) | \(17694720\) | \(2.8157\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.u have rank \(1\).
Complex multiplication
The elliptic curves in class 377520.u do not have complex multiplication.Modular form 377520.2.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 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.
