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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 416025.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
416025.s1 | 416025s2 | \([1, -1, 1, -57781374230, 5346026250458022]\) | \(8000051600110940079507/144453125\) | \(385231210321322021484375\) | \([2]\) | \(794787840\) | \(4.5165\) | \(\Gamma_0(N)\)-optimal* |
416025.s2 | 416025s1 | \([1, -1, 1, -3611452355, 83526680145522]\) | \(1953326569433829507/262451171875\) | \(699911355961704254150390625\) | \([2]\) | \(397393920\) | \(4.1700\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 416025.s have rank \(0\).
Complex multiplication
The elliptic curves in class 416025.s do not have complex multiplication.Modular form 416025.2.a.s
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.