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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 104907j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104907.m2 | 104907j1 | \([0, -1, 1, 23313, 6591980]\) | \(32768/459\) | \(-19627379726720931\) | \([]\) | \(777600\) | \(1.8070\) | \(\Gamma_0(N)\)-optimal |
| 104907.m1 | 104907j2 | \([0, -1, 1, -2074827, 1151651885]\) | \(-23100424192/14739\) | \(-630256971224705451\) | \([]\) | \(2332800\) | \(2.3563\) |
Rank
sage: E.rank()
The elliptic curves in class 104907j have rank \(0\).
Complex multiplication
The elliptic curves in class 104907j do not have complex multiplication.Modular form 104907.2.a.j
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.
