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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 25200.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25200.a1 | 25200dh2 | \([0, 0, 0, -23355, -1372950]\) | \(139798359/98\) | \(987614208000\) | \([2]\) | \(55296\) | \(1.2379\) | |
25200.a2 | 25200dh1 | \([0, 0, 0, -1755, -12150]\) | \(59319/28\) | \(282175488000\) | \([2]\) | \(27648\) | \(0.89132\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25200.a have rank \(1\).
Complex multiplication
The elliptic curves in class 25200.a do not have complex multiplication.Modular form 25200.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.