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SageMath
E = EllipticCurve("ld1")
E.isogeny_class()
Elliptic curves in class 388080.ld
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.ld1 | 388080ld2 | \([0, 0, 0, -756364392, 8006537205324]\) | \(-1647408715474378752/3025\) | \(-87870066867475200\) | \([]\) | \(53996544\) | \(3.3977\) | |
388080.ld2 | 388080ld1 | \([0, 0, 0, -9310392, 11050660124]\) | \(-2239956387422208/27680640625\) | \(-1102971235430988000000\) | \([]\) | \(17998848\) | \(2.8484\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.ld have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.ld do not have complex multiplication.Modular form 388080.2.a.ld
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.