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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 3360z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3360.z3 | 3360z1 | \([0, 1, 0, -5250, 144648]\) | \(250094631024064/62015625\) | \(3969000000\) | \([2, 2]\) | \(3072\) | \(0.82939\) | \(\Gamma_0(N)\)-optimal |
| 3360.z2 | 3360z2 | \([0, 1, 0, -5880, 107100]\) | \(43919722445768/15380859375\) | \(7875000000000\) | \([2]\) | \(6144\) | \(1.1760\) | |
| 3360.z1 | 3360z3 | \([0, 1, 0, -84000, 9342648]\) | \(128025588102048008/7875\) | \(4032000\) | \([2]\) | \(6144\) | \(1.1760\) | |
| 3360.z4 | 3360z4 | \([0, 1, 0, -4625, 181023]\) | \(-2671731885376/1969120125\) | \(-8065516032000\) | \([4]\) | \(6144\) | \(1.1760\) |
Rank
sage: E.rank()
The elliptic curves in class 3360z have rank \(1\).
Complex multiplication
The elliptic curves in class 3360z do not have complex multiplication.Modular form 3360.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
