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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 227430.fu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227430.fu1 | 227430h7 | \([1, -1, 1, -20959367, 23241143409]\) | \(29689921233686449/10380965400750\) | \(356030232260516520036750\) | \([2]\) | \(31850496\) | \(3.2206\) | |
| 227430.fu2 | 227430h4 | \([1, -1, 1, -18717557, 31173602901]\) | \(21145699168383889/2593080\) | \(88933431432436920\) | \([2]\) | \(10616832\) | \(2.6712\) | |
| 227430.fu3 | 227430h6 | \([1, -1, 1, -8775617, -9737831091]\) | \(2179252305146449/66177562500\) | \(2269655281348650562500\) | \([2, 2]\) | \(15925248\) | \(2.8740\) | |
| 227430.fu4 | 227430h3 | \([1, -1, 1, -8710637, -9892977339]\) | \(2131200347946769/2058000\) | \(70582088438442000\) | \([2]\) | \(7962624\) | \(2.5274\) | |
| 227430.fu5 | 227430h2 | \([1, -1, 1, -1172957, 484588581]\) | \(5203798902289/57153600\) | \(1960165427490446400\) | \([2, 2]\) | \(5308416\) | \(2.3247\) | |
| 227430.fu6 | 227430h5 | \([1, -1, 1, -263237, 1216367349]\) | \(-58818484369/18600435000\) | \(-637928837785953315000\) | \([2]\) | \(10616832\) | \(2.6712\) | |
| 227430.fu7 | 227430h1 | \([1, -1, 1, -133277, -6556251]\) | \(7633736209/3870720\) | \(132751944295649280\) | \([2]\) | \(2654208\) | \(1.9781\) | \(\Gamma_0(N)\)-optimal |
| 227430.fu8 | 227430h8 | \([1, -1, 1, 2368453, -32788225479]\) | \(42841933504271/13565917968750\) | \(-465262789999495605468750\) | \([2]\) | \(31850496\) | \(3.2206\) |
Rank
sage: E.rank()
The elliptic curves in class 227430.fu have rank \(0\).
Complex multiplication
The elliptic curves in class 227430.fu do not have complex multiplication.Modular form 227430.2.a.fu
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
