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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 6720.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6720.v1 | 6720bp3 | \([0, -1, 0, -262305, -51618303]\) | \(60910917333827912/3255076125\) | \(106662334464000\) | \([2]\) | \(36864\) | \(1.7591\) | |
| 6720.v2 | 6720bp2 | \([0, -1, 0, -17305, -707303]\) | \(139927692143296/27348890625\) | \(112021056000000\) | \([2, 2]\) | \(18432\) | \(1.4126\) | |
| 6720.v3 | 6720bp1 | \([0, -1, 0, -5300, 140250]\) | \(257307998572864/19456203375\) | \(1245197016000\) | \([2]\) | \(9216\) | \(1.0660\) | \(\Gamma_0(N)\)-optimal |
| 6720.v4 | 6720bp4 | \([0, -1, 0, 35615, -4231775]\) | \(152461584507448/322998046875\) | \(-10584000000000000\) | \([4]\) | \(36864\) | \(1.7591\) |
Rank
sage: E.rank()
The elliptic curves in class 6720.v have rank \(1\).
Complex multiplication
The elliptic curves in class 6720.v do not have complex multiplication.Modular form 6720.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
