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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3360c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3360.c3 | 3360c1 | \([0, -1, 0, -19846, -1069280]\) | \(13507798771700416/3544416225\) | \(226842638400\) | \([2, 2]\) | \(7680\) | \(1.1637\) | \(\Gamma_0(N)\)-optimal |
| 3360.c1 | 3360c2 | \([0, -1, 0, -317521, -68760575]\) | \(864335783029582144/59535\) | \(243855360\) | \([2]\) | \(15360\) | \(1.5103\) | |
| 3360.c2 | 3360c3 | \([0, -1, 0, -22296, -786060]\) | \(2394165105226952/854262178245\) | \(437382235261440\) | \([2]\) | \(15360\) | \(1.5103\) | |
| 3360.c4 | 3360c4 | \([0, -1, 0, -17416, -1343384]\) | \(-1141100604753992/875529151875\) | \(-448270925760000\) | \([2]\) | \(15360\) | \(1.5103\) |
Rank
sage: E.rank()
The elliptic curves in class 3360c have rank \(1\).
Complex multiplication
The elliptic curves in class 3360c do not have complex multiplication.Modular form 3360.2.a.c
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.
