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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 95370t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.r1 | 95370t1 | \([1, 1, 0, -2457517, 1481792521]\) | \(68001744211490809/1022422500\) | \(24678793640902500\) | \([2]\) | \(2322432\) | \(2.2820\) | \(\Gamma_0(N)\)-optimal |
95370.r2 | 95370t2 | \([1, 1, 0, -2385267, 1573102071]\) | \(-62178675647294809/8362782148050\) | \(-201857231130525090450\) | \([2]\) | \(4644864\) | \(2.6286\) |
Rank
sage: E.rank()
The elliptic curves in class 95370t have rank \(1\).
Complex multiplication
The elliptic curves in class 95370t do not have complex multiplication.Modular form 95370.2.a.t
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.