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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 15600d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.m4 | 15600d1 | \([0, -1, 0, 2092, -26688]\) | \(253012016/219375\) | \(-877500000000\) | \([2]\) | \(18432\) | \(0.97923\) | \(\Gamma_0(N)\)-optimal |
| 15600.m3 | 15600d2 | \([0, -1, 0, -10408, -226688]\) | \(7793764996/3080025\) | \(49280400000000\) | \([2, 2]\) | \(36864\) | \(1.3258\) | |
| 15600.m1 | 15600d3 | \([0, -1, 0, -145408, -21286688]\) | \(10625310339698/3855735\) | \(123383520000000\) | \([2]\) | \(73728\) | \(1.6724\) | |
| 15600.m2 | 15600d4 | \([0, -1, 0, -75408, 7833312]\) | \(1481943889298/34543665\) | \(1105397280000000\) | \([2]\) | \(73728\) | \(1.6724\) |
Rank
sage: E.rank()
The elliptic curves in class 15600d have rank \(1\).
Complex multiplication
The elliptic curves in class 15600d do not have complex multiplication.Modular form 15600.2.a.d
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.
