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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 258570.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
258570.a1 | 258570a2 | \([1, -1, 0, -138735, 9271341]\) | \(2397007293813769/1088000000000\) | \(134042688000000000\) | \([]\) | \(4976640\) | \(1.9815\) | |
258570.a2 | 258570a1 | \([1, -1, 0, -69120, -6976800]\) | \(296431397798809/19652000\) | \(2421146052000\) | \([]\) | \(1658880\) | \(1.4322\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 258570.a have rank \(0\).
Complex multiplication
The elliptic curves in class 258570.a do not have complex multiplication.Modular form 258570.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.