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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 361998.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361998.w1 | 361998w4 | \([1, -1, 0, -60706437, -175147540723]\) | \(260421323354494875/11193459697784\) | \(1063446744840724679191848\) | \([2]\) | \(52254720\) | \(3.3742\) | |
| 361998.w2 | 361998w2 | \([1, -1, 0, -9296637, 10843290693]\) | \(681832159429723875/4999492918784\) | \(651553130227217766912\) | \([2]\) | \(17418240\) | \(2.8249\) | |
| 361998.w3 | 361998w1 | \([1, -1, 0, -211197, 382315077]\) | \(-7994001499875/479749996544\) | \(-62522863228850798592\) | \([2]\) | \(8709120\) | \(2.4783\) | \(\Gamma_0(N)\)-optimal |
| 361998.w4 | 361998w3 | \([1, -1, 0, 1897923, -10235135611]\) | \(7958073457125/480903934784\) | \(-45688798444361873830848\) | \([2]\) | \(26127360\) | \(3.0276\) |
Rank
sage: E.rank()
The elliptic curves in class 361998.w have rank \(1\).
Complex multiplication
The elliptic curves in class 361998.w do not have complex multiplication.Modular form 361998.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
