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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1360e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1360.g1 | 1360e1 | \([0, 0, 0, -28, -57]\) | \(151732224/85\) | \(1360\) | \([2]\) | \(96\) | \(-0.45155\) | \(\Gamma_0(N)\)-optimal |
1360.g2 | 1360e2 | \([0, 0, 0, -23, -78]\) | \(-5256144/7225\) | \(-1849600\) | \([2]\) | \(192\) | \(-0.10497\) |
Rank
sage: E.rank()
The elliptic curves in class 1360e have rank \(1\).
Complex multiplication
The elliptic curves in class 1360e do not have complex multiplication.Modular form 1360.2.a.e
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.