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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 257400o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257400.o2 | 257400o1 | \([0, 0, 0, 329325, -90369250]\) | \(338649393884/498444375\) | \(-5813855190000000000\) | \([2]\) | \(5308416\) | \(2.2860\) | \(\Gamma_0(N)\)-optimal |
257400.o1 | 257400o2 | \([0, 0, 0, -2145675, -904644250]\) | \(46831495741058/11946352275\) | \(278684505871200000000\) | \([2]\) | \(10616832\) | \(2.6326\) |
Rank
sage: E.rank()
The elliptic curves in class 257400o have rank \(0\).
Complex multiplication
The elliptic curves in class 257400o do not have complex multiplication.Modular form 257400.2.a.o
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.