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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 38646w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38646.u2 | 38646w1 | \([1, -1, 1, -37436, -2732353]\) | \(7958910549046393/151342682688\) | \(110328815679552\) | \([2]\) | \(165888\) | \(1.4879\) | \(\Gamma_0(N)\)-optimal |
| 38646.u1 | 38646w2 | \([1, -1, 1, -78116, 4297151]\) | \(72312097990757113/31003988313096\) | \(22601907480246984\) | \([2]\) | \(331776\) | \(1.8345\) |
Rank
sage: E.rank()
The elliptic curves in class 38646w have rank \(1\).
Complex multiplication
The elliptic curves in class 38646w do not have complex multiplication.Modular form 38646.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
