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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 310464.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.t1 | 310464t2 | \([0, 0, 0, -59052, -5523280]\) | \(1389715708/11\) | \(180257882112\) | \([2]\) | \(1179648\) | \(1.3324\) | |
310464.t2 | 310464t1 | \([0, 0, 0, -3612, -90160]\) | \(-1272112/121\) | \(-495709175808\) | \([2]\) | \(589824\) | \(0.98579\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.t have rank \(0\).
Complex multiplication
The elliptic curves in class 310464.t do not have complex multiplication.Modular form 310464.2.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.