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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 176400ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.qw2 | 176400ck1 | \([0, 0, 0, 18375, 2786875]\) | \(1280/7\) | \(-3752267793750000\) | \([]\) | \(829440\) | \(1.6705\) | \(\Gamma_0(N)\)-optimal |
| 176400.qw1 | 176400ck2 | \([0, 0, 0, -1084125, 434966875]\) | \(-262885120/343\) | \(-183861121893750000\) | \([]\) | \(2488320\) | \(2.2198\) |
Rank
sage: E.rank()
The elliptic curves in class 176400ck have rank \(1\).
Complex multiplication
The elliptic curves in class 176400ck do not have complex multiplication.Modular form 176400.2.a.ck
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.
