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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 94192.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94192.t1 | 94192n1 | \([0, 1, 0, -512, -4684]\) | \(-4317433/56\) | \(-192905216\) | \([]\) | \(25920\) | \(0.39864\) | \(\Gamma_0(N)\)-optimal |
94192.t2 | 94192n2 | \([0, 1, 0, 1808, -22316]\) | \(189636887/175616\) | \(-604950757376\) | \([]\) | \(77760\) | \(0.94795\) |
Rank
sage: E.rank()
The elliptic curves in class 94192.t have rank \(2\).
Complex multiplication
The elliptic curves in class 94192.t do not have complex multiplication.Modular form 94192.2.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.