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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 137904.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137904.t1 | 137904bm1 | \([0, -1, 0, -1213, -15887]\) | \(-4566016000/7803\) | \(-337588992\) | \([]\) | \(51840\) | \(0.53108\) | \(\Gamma_0(N)\)-optimal |
| 137904.t2 | 137904bm2 | \([0, -1, 0, 1907, -79535]\) | \(17718272000/72412707\) | \(-3132863355648\) | \([]\) | \(155520\) | \(1.0804\) |
Rank
sage: E.rank()
The elliptic curves in class 137904.t have rank \(0\).
Complex multiplication
The elliptic curves in class 137904.t do not have complex multiplication.Modular form 137904.2.a.t
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.
