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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 193600ew
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193600.io2 | 193600ew1 | \([0, -1, 0, 576767, 63794337]\) | \(24167/16\) | \(-14048223625216000000\) | \([]\) | \(3649536\) | \(2.3629\) | \(\Gamma_0(N)\)-optimal |
| 193600.io1 | 193600ew2 | \([0, -1, 0, -10071233, 12639082337]\) | \(-128667913/4096\) | \(-3596345248055296000000\) | \([]\) | \(10948608\) | \(2.9122\) |
Rank
sage: E.rank()
The elliptic curves in class 193600ew have rank \(1\).
Complex multiplication
The elliptic curves in class 193600ew do not have complex multiplication.Modular form 193600.2.a.ew
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
