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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 388080.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.s1 | 388080s2 | \([0, 0, 0, -562863, -220176502]\) | \(-18330740176/8857805\) | \(-9529671474123736320\) | \([]\) | \(8709120\) | \(2.3473\) | |
| 388080.s2 | 388080s1 | \([0, 0, 0, 54537, 3692738]\) | \(16674224/15125\) | \(-16272234605088000\) | \([]\) | \(2903040\) | \(1.7980\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.s have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.s do not have complex multiplication.Modular form 388080.2.a.s
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.
