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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 117117.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117117.t1 | 117117cb1 | \([1, -1, 1, -149, -412]\) | \(226981/77\) | \(123324201\) | \([2]\) | \(31104\) | \(0.25473\) | \(\Gamma_0(N)\)-optimal |
117117.t2 | 117117cb2 | \([1, -1, 1, 436, -3220]\) | \(5735339/5929\) | \(-9495963477\) | \([2]\) | \(62208\) | \(0.60130\) |
Rank
sage: E.rank()
The elliptic curves in class 117117.t have rank \(1\).
Complex multiplication
The elliptic curves in class 117117.t do not have complex multiplication.Modular form 117117.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.