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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 22800.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22800.e1 | 22800m2 | \([0, -1, 0, -928, 11152]\) | \(691234772/3249\) | \(415872000\) | \([2]\) | \(10240\) | \(0.50358\) | |
22800.e2 | 22800m1 | \([0, -1, 0, -28, 352]\) | \(-78608/1539\) | \(-49248000\) | \([2]\) | \(5120\) | \(0.15700\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22800.e have rank \(2\).
Complex multiplication
The elliptic curves in class 22800.e do not have complex multiplication.Modular form 22800.2.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 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.