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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 270802v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270802.v2 | 270802v1 | \([1, 1, 1, 32361, -7960675]\) | \(6300872423/49827568\) | \(-29638599475113328\) | \([2]\) | \(2150400\) | \(1.8421\) | \(\Gamma_0(N)\)-optimal |
270802.v1 | 270802v2 | \([1, 1, 1, -455419, -108833579]\) | \(17561807821657/1590616244\) | \(946135636692626324\) | \([2]\) | \(4300800\) | \(2.1887\) |
Rank
sage: E.rank()
The elliptic curves in class 270802v have rank \(0\).
Complex multiplication
The elliptic curves in class 270802v do not have complex multiplication.Modular form 270802.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.