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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 51376t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51376.o4 | 51376t1 | \([0, 0, 0, 10309, -136214]\) | \(6128487/3952\) | \(-78133449392128\) | \([2]\) | \(137088\) | \(1.3547\) | \(\Gamma_0(N)\)-optimal |
51376.o3 | 51376t2 | \([0, 0, 0, -43771, -1120470]\) | \(469097433/244036\) | \(4824740499963904\) | \([2, 2]\) | \(274176\) | \(1.7013\) | |
51376.o2 | 51376t3 | \([0, 0, 0, -395291, 94844490]\) | \(345505073913/3388346\) | \(66989666172575744\) | \([4]\) | \(548352\) | \(2.0479\) | |
51376.o1 | 51376t4 | \([0, 0, 0, -557531, -160077814]\) | \(969417177273/1085318\) | \(21457398539313152\) | \([2]\) | \(548352\) | \(2.0479\) |
Rank
sage: E.rank()
The elliptic curves in class 51376t have rank \(1\).
Complex multiplication
The elliptic curves in class 51376t do not have complex multiplication.Modular form 51376.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.