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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 195195c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 195195.p4 | 195195c1 | \([1, 0, 0, -595, -40600]\) | \(-4826809/144375\) | \(-696870549375\) | \([2]\) | \(221184\) | \(0.95292\) | \(\Gamma_0(N)\)-optimal |
| 195195.p3 | 195195c2 | \([1, 0, 0, -21720, -1227825]\) | \(234770924809/1334025\) | \(6439083876225\) | \([2, 2]\) | \(442368\) | \(1.2995\) | |
| 195195.p2 | 195195c3 | \([1, 0, 0, -34395, 366690]\) | \(932288503609/527295615\) | \(2545155220142535\) | \([2]\) | \(884736\) | \(1.6461\) | |
| 195195.p1 | 195195c4 | \([1, 0, 0, -347045, -78720240]\) | \(957681397954009/31185\) | \(150524038665\) | \([2]\) | \(884736\) | \(1.6461\) |
Rank
sage: E.rank()
The elliptic curves in class 195195c have rank \(0\).
Complex multiplication
The elliptic curves in class 195195c do not have complex multiplication.Modular form 195195.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
