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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 73960.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73960.a1 | 73960b4 | \([0, 0, 0, -197843, 33869982]\) | \(132304644/5\) | \(32365378810880\) | \([2]\) | \(314496\) | \(1.6784\) | |
73960.a2 | 73960b2 | \([0, 0, 0, -12943, 477042]\) | \(148176/25\) | \(40456723513600\) | \([2, 2]\) | \(157248\) | \(1.3318\) | |
73960.a3 | 73960b1 | \([0, 0, 0, -3698, -79507]\) | \(55296/5\) | \(505709043920\) | \([2]\) | \(78624\) | \(0.98524\) | \(\Gamma_0(N)\)-optimal |
73960.a4 | 73960b3 | \([0, 0, 0, 24037, 2703238]\) | \(237276/625\) | \(-4045672351360000\) | \([2]\) | \(314496\) | \(1.6784\) |
Rank
sage: E.rank()
The elliptic curves in class 73960.a have rank \(1\).
Complex multiplication
The elliptic curves in class 73960.a do not have complex multiplication.Modular form 73960.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.