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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 38646.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38646.t1 | 38646o2 | \([1, -1, 1, -1634861, 804988541]\) | \(17897905066884975025011/4805830835912\) | \(129757432569624\) | \([2]\) | \(442368\) | \(2.0792\) | |
38646.t2 | 38646o1 | \([1, -1, 1, -102581, 12493325]\) | \(4421369023022205171/71573878342336\) | \(1932494715243072\) | \([2]\) | \(221184\) | \(1.7327\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38646.t have rank \(0\).
Complex multiplication
The elliptic curves in class 38646.t do not have complex multiplication.Modular form 38646.2.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.