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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 50960.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50960.g1 | 50960y3 | \([0, 1, 0, -162696, -24299276]\) | \(988345570681/44994560\) | \(21682442196746240\) | \([2]\) | \(497664\) | \(1.8966\) | |
| 50960.g2 | 50960y1 | \([0, 1, 0, -25496, 1549204]\) | \(3803721481/26000\) | \(12529147904000\) | \([2]\) | \(165888\) | \(1.3472\) | \(\Gamma_0(N)\)-optimal |
| 50960.g3 | 50960y2 | \([0, 1, 0, -9816, 3449620]\) | \(-217081801/10562500\) | \(-5089966336000000\) | \([2]\) | \(331776\) | \(1.6938\) | |
| 50960.g4 | 50960y4 | \([0, 1, 0, 88184, -92237580]\) | \(157376536199/7722894400\) | \(-3721587930175897600\) | \([2]\) | \(995328\) | \(2.2431\) |
Rank
sage: E.rank()
The elliptic curves in class 50960.g have rank \(1\).
Complex multiplication
The elliptic curves in class 50960.g do not have complex multiplication.Modular form 50960.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
