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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 24563e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24563.b2 | 24563e1 | \([1, 1, 1, -1152, -16312]\) | \(-95443993/5887\) | \(-10429179607\) | \([2]\) | \(15360\) | \(0.67674\) | \(\Gamma_0(N)\)-optimal |
24563.b1 | 24563e2 | \([1, 1, 1, -18697, -991814]\) | \(408023180713/1421\) | \(2517388181\) | \([2]\) | \(30720\) | \(1.0233\) |
Rank
sage: E.rank()
The elliptic curves in class 24563e have rank \(1\).
Complex multiplication
The elliptic curves in class 24563e do not have complex multiplication.Modular form 24563.2.a.e
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.