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SageMath
E = EllipticCurve("mv1")
E.isogeny_class()
Elliptic curves in class 487872mv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 487872.mv4 | 487872mv1 | \([0, 0, 0, -44920524, 38336271248]\) | \(29609739866953/15259926528\) | \(5166256965603919562539008\) | \([2]\) | \(88473600\) | \(3.4341\) | \(\Gamma_0(N)\)-optimal |
| 487872.mv2 | 487872mv2 | \([0, 0, 0, -401764044, -3072054586480]\) | \(21184262604460873/216872764416\) | \(73422400019954923235966976\) | \([2, 2]\) | \(176947200\) | \(3.7807\) | |
| 487872.mv3 | 487872mv3 | \([0, 0, 0, -100677324, -7569688009840]\) | \(-333345918055753/72923718045024\) | \(-24688366986339495663699492864\) | \([2]\) | \(353894400\) | \(4.1273\) | |
| 487872.mv1 | 487872mv4 | \([0, 0, 0, -6412347084, -197639436057712]\) | \(86129359107301290313/9166294368\) | \(3103254268004820213301248\) | \([2]\) | \(353894400\) | \(4.1273\) |
Rank
sage: E.rank()
The elliptic curves in class 487872mv have rank \(0\).
Complex multiplication
The elliptic curves in class 487872mv do not have complex multiplication.Modular form 487872.2.a.mv
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.
