Show commands:
SageMath
E = EllipticCurve("tq1")
E.isogeny_class()
Elliptic curves in class 435600.tq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435600.tq1 | 435600tq2 | \([0, 0, 0, -8575875, -9658068750]\) | \(1000188\) | \(69739270326000000000\) | \([2]\) | \(19660800\) | \(2.7270\) | \(\Gamma_0(N)\)-optimal* |
435600.tq2 | 435600tq1 | \([0, 0, 0, -408375, -224606250]\) | \(-432\) | \(-17434817581500000000\) | \([2]\) | \(9830400\) | \(2.3805\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435600.tq have rank \(1\).
Complex multiplication
The elliptic curves in class 435600.tq do not have complex multiplication.Modular form 435600.2.a.tq
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.