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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 433200.fl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433200.fl1 | 433200fl3 | \([0, -1, 0, -438979008, 3540231760512]\) | \(3107086841064961/570\) | \(1716233738880000000\) | \([4]\) | \(79626240\) | \(3.3346\) | \(\Gamma_0(N)\)-optimal* |
433200.fl2 | 433200fl4 | \([0, -1, 0, -31771008, 36683440512]\) | \(1177918188481/488703750\) | \(1471455901872240000000000\) | \([2]\) | \(79626240\) | \(3.3346\) | |
433200.fl3 | 433200fl2 | \([0, -1, 0, -27439008, 55311040512]\) | \(758800078561/324900\) | \(978253231161600000000\) | \([2, 2]\) | \(39813120\) | \(2.9880\) | \(\Gamma_0(N)\)-optimal* |
433200.fl4 | 433200fl1 | \([0, -1, 0, -1447008, 1143712512]\) | \(-111284641/123120\) | \(-370706487598080000000\) | \([2]\) | \(19906560\) | \(2.6415\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 433200.fl have rank \(1\).
Complex multiplication
The elliptic curves in class 433200.fl do not have complex multiplication.Modular form 433200.2.a.fl
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.