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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 53040z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53040.cu1 | 53040z1 | \([0, 1, 0, -3089195, 2088807468]\) | \(203769809659907949070336/2016474841511325\) | \(32263597464181200\) | \([2]\) | \(1013760\) | \(2.3277\) | \(\Gamma_0(N)\)-optimal |
53040.cu2 | 53040z2 | \([0, 1, 0, -3015500, 2193277500]\) | \(-11845731628994222232016/1269935194601506875\) | \(-325103409817985760000\) | \([2]\) | \(2027520\) | \(2.6743\) |
Rank
sage: E.rank()
The elliptic curves in class 53040z have rank \(0\).
Complex multiplication
The elliptic curves in class 53040z do not have complex multiplication.Modular form 53040.2.a.z
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.