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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 270400el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270400.el2 | 270400el1 | \([0, 0, 0, -23660, -878800]\) | \(37044/13\) | \(514035851264000\) | \([2]\) | \(860160\) | \(1.5241\) | \(\Gamma_0(N)\)-optimal |
270400.el1 | 270400el2 | \([0, 0, 0, -158860, 23727600]\) | \(5606442/169\) | \(13364932132864000\) | \([2]\) | \(1720320\) | \(1.8707\) |
Rank
sage: E.rank()
The elliptic curves in class 270400el have rank \(2\).
Complex multiplication
The elliptic curves in class 270400el do not have complex multiplication.Modular form 270400.2.a.el
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.