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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 101430.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.e1 | 101430bs1 | \([1, -1, 0, -135, 1021]\) | \(-7649089/7360\) | \(-262906560\) | \([]\) | \(51840\) | \(0.31176\) | \(\Gamma_0(N)\)-optimal |
101430.e2 | 101430bs2 | \([1, -1, 0, 1125, -17375]\) | \(4405959551/6083500\) | \(-217308703500\) | \([]\) | \(155520\) | \(0.86106\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.e have rank \(2\).
Complex multiplication
The elliptic curves in class 101430.e do not have complex multiplication.Modular form 101430.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.