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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 148720w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148720.bm2 | 148720w1 | \([0, 1, 0, 26984, 6896020]\) | \(109902239/1100000\) | \(-21747670630400000\) | \([]\) | \(921600\) | \(1.8160\) | \(\Gamma_0(N)\)-optimal |
148720.bm1 | 148720w2 | \([0, 1, 0, -16061816, 24771155540]\) | \(-23178622194826561/1610510\) | \(-31840764569968640\) | \([]\) | \(4608000\) | \(2.6207\) |
Rank
sage: E.rank()
The elliptic curves in class 148720w have rank \(1\).
Complex multiplication
The elliptic curves in class 148720w do not have complex multiplication.Modular form 148720.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.