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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 277200.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.cl1 | 277200cl3 | \([0, 0, 0, -3171675, 2174098250]\) | \(75627935783569/396165\) | \(18483474240000000\) | \([2]\) | \(4718592\) | \(2.3173\) | |
| 277200.cl2 | 277200cl2 | \([0, 0, 0, -201675, 32728250]\) | \(19443408769/1334025\) | \(62240270400000000\) | \([2, 2]\) | \(2359296\) | \(1.9707\) | |
| 277200.cl3 | 277200cl1 | \([0, 0, 0, -39675, -2425750]\) | \(148035889/31185\) | \(1454967360000000\) | \([2]\) | \(1179648\) | \(1.6242\) | \(\Gamma_0(N)\)-optimal |
| 277200.cl4 | 277200cl4 | \([0, 0, 0, 176325, 141214250]\) | \(12994449551/192163125\) | \(-8965562760000000000\) | \([2]\) | \(4718592\) | \(2.3173\) |
Rank
sage: E.rank()
The elliptic curves in class 277200.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.cl do not have complex multiplication.Modular form 277200.2.a.cl
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.
