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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 152460ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.o4 | 152460ca1 | \([0, 0, 0, -42108, -3323507]\) | \(10788913152/8575\) | \(6562570568400\) | \([2]\) | \(414720\) | \(1.3897\) | \(\Gamma_0(N)\)-optimal |
| 152460.o3 | 152460ca2 | \([0, 0, 0, -51183, -1786202]\) | \(1210991472/588245\) | \(7203077455875840\) | \([2]\) | \(829440\) | \(1.7363\) | |
| 152460.o2 | 152460ca3 | \([0, 0, 0, -143748, 17285697]\) | \(588791808/109375\) | \(61021861535250000\) | \([2]\) | \(1244160\) | \(1.9390\) | |
| 152460.o1 | 152460ca4 | \([0, 0, 0, -2185623, 1243635822]\) | \(129348709488/6125\) | \(54675587935584000\) | \([2]\) | \(2488320\) | \(2.2856\) |
Rank
sage: E.rank()
The elliptic curves in class 152460ca have rank \(1\).
Complex multiplication
The elliptic curves in class 152460ca do not have complex multiplication.Modular form 152460.2.a.ca
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
