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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 3150.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.i1 | 3150l6 | \([1, -1, 0, -614367, 185502541]\) | \(2251439055699625/25088\) | \(285768000000\) | \([2]\) | \(20736\) | \(1.7671\) | |
| 3150.i2 | 3150l5 | \([1, -1, 0, -38367, 2910541]\) | \(-548347731625/1835008\) | \(-20901888000000\) | \([2]\) | \(10368\) | \(1.4206\) | |
| 3150.i3 | 3150l4 | \([1, -1, 0, -7992, 227416]\) | \(4956477625/941192\) | \(10720765125000\) | \([2]\) | \(6912\) | \(1.2178\) | |
| 3150.i4 | 3150l2 | \([1, -1, 0, -2367, -43709]\) | \(128787625/98\) | \(1116281250\) | \([2]\) | \(2304\) | \(0.66851\) | |
| 3150.i5 | 3150l1 | \([1, -1, 0, -117, -959]\) | \(-15625/28\) | \(-318937500\) | \([2]\) | \(1152\) | \(0.32194\) | \(\Gamma_0(N)\)-optimal |
| 3150.i6 | 3150l3 | \([1, -1, 0, 1008, 20416]\) | \(9938375/21952\) | \(-250047000000\) | \([2]\) | \(3456\) | \(0.87125\) |
Rank
sage: E.rank()
The elliptic curves in class 3150.i have rank \(0\).
Complex multiplication
The elliptic curves in class 3150.i do not have complex multiplication.Modular form 3150.2.a.i
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
