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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 52416.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52416.t1 | 52416w2 | \([0, 0, 0, -12204, -797904]\) | \(-38958219/30758\) | \(-158704524066816\) | \([]\) | \(165888\) | \(1.4234\) | |
52416.t2 | 52416w1 | \([0, 0, 0, 1236, 17456]\) | \(29503629/35672\) | \(-252482420736\) | \([]\) | \(55296\) | \(0.87406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 52416.t have rank \(2\).
Complex multiplication
The elliptic curves in class 52416.t do not have complex multiplication.Modular form 52416.2.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.