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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 26520.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26520.z1 | 26520bb4 | \([0, 1, 0, -2040056, -1122211200]\) | \(916959671620739147236/2731145625\) | \(2796693120000\) | \([2]\) | \(393216\) | \(2.0417\) | |
26520.z2 | 26520bb2 | \([0, 1, 0, -127556, -17551200]\) | \(896581610757188944/1545359765625\) | \(395612100000000\) | \([2, 2]\) | \(196608\) | \(1.6951\) | |
26520.z3 | 26520bb3 | \([0, 1, 0, -87776, -28657776]\) | \(-73039208963041156/303497314453125\) | \(-310781250000000000\) | \([2]\) | \(393216\) | \(2.0417\) | |
26520.z4 | 26520bb1 | \([0, 1, 0, -10511, -88086]\) | \(8027441608013824/4452347908125\) | \(71237566530000\) | \([4]\) | \(98304\) | \(1.3485\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26520.z have rank \(1\).
Complex multiplication
The elliptic curves in class 26520.z do not have complex multiplication.Modular form 26520.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.